<> For the two sides to be equal, the corresponding coefficients must be equal. where [latex]\left(h,\text{ }k\right)[/latex] is the vertex. �R1�a�Pm3C�'(�|h�%� �T3� ��`'[Yp All function rules can be described as a transformation of an original function rule. You can use transformations of quadratic functions to analyze changes in braking distance. The vertex formof a quadratic function is f(x) =a(x−h)2+k, where a≠ 0 and the vertex is (h, k). Some of the topics tested under this chapter are - Identity, Completing the Square, Discriminant, Repeated Roots, Factorization, and Formation of New Equations. ­ Find the x­value of the vertex (when in standard form use ) ­ Place this value in the middle of your table. Remember, the QUADRATIC PARENT FUNCTION is f (x) = ¿ _____ Let’s graph the quadratic parent function! Google Classroom Facebook Twitter. Transformations with Quadratic Functions. The equation for the graph of [latex]f(x)=x^2[/latex] that has been shifted right 2 units is, The equation for the graph of [latex]f(x)=^2[/latex] that has been shifted left 2 units is. Quadratic equations are equations of the form y = ax 2 + bx + c or y = a(x - h) 2 + k. The shape of the graph of a quadratic equation is a parabola. Lesson 1 Modeling Data with Quadratic Functions. [latex]\begin{align}&a{\left(x-h\right)}^{2}+k=a{x}^{2}+bx+c\\ &a{x}^{2}-2ahx+\left(a{h}^{2}+k\right)=a{x}^{2}+bx+c \end{align}[/latex]. 23 0 obj endobj %���� Also, determine the equation for the graph of [latex]f(x)=x^2[/latex] that has been vertically stretched by a factor of 3. Dividing Polynomials; ... Show Mobile Notice Show All Notes Hide All Notes. Also, determine the equation for the graph of [latex]f(x)=x^2[/latex] that has been shifted left 2 units. 2. Lesson 2 Properties of Parabolas. The equation for the graph of [latex]f(x)=x^2[/latex] that has been shifted up 4 units is, The equation for the graph of [latex]f(x)=x^2[/latex] that has been shifted down 4 units is. Honors Algebra 2 Notes: Graphs of Quadratic Functions Transformations/Intro to … LESSON 19: Transformations with Quadratic FunctionsLESSON 20: Modeling With Quadratic FunctionsLESSON 21: Projectile Problems & Review. The equation for the quadratic function is y x= 2 and its graph is a bowl-shaped curve called a parabola. Class Notes. Just like Transformations in Geometry, we can move and resize the graphs of functions: Let us start with a function, in this case it is f(x) = x 2, but it could be anything: f(x) = x 2. ... Notes for graphing quadratic functions AND homework worksheet. We’d love your input. Vertex: Opens Up or Down? The standard form of a quadratic function presents the function in the form. Graph by using a table. If [latex]h>0[/latex], the graph shifts toward the right and if [latex]h<0[/latex], the graph shifts to the left. Quadratic functions are second order functions, meaning the highest exponent for a variable is two. 1. 5.5: Complex Numbers and Roots. Graphing Quadratic Equations Using Transformations A quadratic equation is a polynomial equation of degree 2 . Then graph each of the following quadratic functions and describe the transformation. Also, determine the equation for the graph of [latex]f(x)=x^2[/latex] that has been shifted down 4 units. endstream The U-shaped graph of a quadratic function is called a parabola. We can see this by expanding out the general form and setting it equal to the standard form. Graph vertical compressions and stretches of quadratic functions. Factoring Flow Chart . In particular, the coefficients of [latex]x[/latex] must be equal. They're usually in this form: f(x) = ax 2 + bx + … Unit 5 Notes Day 02 – Transformations of Quadratic Functions a – h – b – k – We worked a little bit with QUADRATIC FUNCTIONS back in Unit 2 when we were learning transformations. 5.1: Using Transformations to Graph Quadratic Functions. %PDF-1.4 Must Read: 2013Chapter 5.1-5.4 Review 2013 Solving Quadratic Equations by Factoring, Quad Formula and +/- Square Roots Review of Quadratic Functions and completing the square ... Transformations of Functions This video explains transformation of the basic quadratic function.http://mathispower4u.com Here are some simple things we can do to move or scale it on the graph: We also realize students learn best in a safe and caring environment, which includes being respectful of others, regardless of race, gender, and socio-economic status. The standard form of a quadratic function presents the function in the form, [latex]f\left(x\right)=a{\left(x-h\right)}^{2}+k[/latex]. Because the vertex appears in the standard form of the quadratic function, this form is also known as the vertex form of a quadratic function. Last word on Chapt. You can represent a stretch or compression (narrowing, widening) of the graph of [latex]f(x)=x^2[/latex] by multiplying the squared variable by a constant, [latex]a[/latex]. stream Notes 4­7 Transforming Exponential and Logarithmic Functions ... You can provide the same transformations on exponential functions as you performed on polynomial, quadratic and linear functions... 3 Ex. The graphing calculator is used to confirm hypotheses about the effect of “a” on x 2 and then the functions are sketched in their notes using the three points highlighted on the parent function. The figure below is the graph of this basic function. <> Email. The best way to graph quadratic functions is to: 1) Identify and plot the vertex, Lesson 11.7 - "More Than Meets the Eye" - Transformations of Quadratic Functions 11.7 Guided Notes - Transformations of Quadratic Functions 11.7 Guided Notes - Transformations of Quadratic Functions - Answer Key 11.7 Classwork - Transformations of Quadratic Functions 11.7 Classwork - Transformations of Quadratic Functions - Answer Key �B�eYp�E1! Determine the equation for the graph of [latex]f(x)=x^2[/latex] that has been shifted up 4 units. The Parent Function is the simplest function with the defining characteristics of the family. If [latex]|a|>1[/latex], the point associated with a particular [latex]x[/latex]-value shifts farther from the [latex]x[/latex]–axis, so the graph appears to become narrower, and there is a vertical stretch. Algebra Unit 6: Graphing Quadratic Functions Notes 1 Day 1: Quadratic Transformations (H & K values) The parent function of a function is the simplest form of a function. A quadratic transformation relates two hypergeometric functions, with the variable in one a quadratic function of the variable in the other, possibly combined with a fractional linear transformation. But if [latex]|a|<1[/latex], the point associated with a particular [latex]x[/latex]-value shifts closer to the [latex]x[/latex]–axis, so the graph appears to become wider, but in fact there is a vertical compression. The standard form is useful for determining how the graph is transformed from the graph of [latex]y={x}^{2}[/latex]. (credit: modification of work by Dan Meyer). Read the article to find notes for Quadratic Equation for JEE Main preparation. "=" Transformations include reflections, translations (both vertical and … Assignment #27 Practice Quiz . Determine the equation for the graph of [latex]f(x)=x^2[/latex] that has been shifted right 2 units. The parent graph of a quadratic function is y = x2. Transforming quadratic functions. When comparing the two graphs, you can see that it was reflected over the x-axis and translated to the right 4 units and translated down 1 unit. I ask that you join me and the staff at YHS in working to help assure success and safety for all students who attend YHS. 5.3: Solving Quadratic Equations by Graphing and Factoring. If [latex]k>0[/latex], the graph shifts upward, whereas if [latex]k<0[/latex], the graph shifts downward. Jw��nY���~�a��H�J/W�j���������r� &L�0a„ &L�0a„ &L�0a„ &L�0a„ &L�0a„ &L�0a„ &L�0a„���V Warm Up. Lesson 4 Factoring Quadratic Expressions. The parent function for a quadratic function is y = x 2 or f(x) = x. Graph the parent function below. Your Algebra 2 Honors students will have foldables, guided notes, homework, and a content quiz in the Quadratic Functions & Transformations lesson of a ten lesson unit on Quadratic Functions & Equations that cover the concepts in depth.Students will be able to:★ Describe and graph transforma Section 2-5 : Quadratic Equations - Part I. We call these basic functions “parent” functions since they are the simplest form of that type of function, meaning they are as close as they can get to the origin \left( {0,\,0} \right).The chart below provides some basic parent functions that you should be familiar with. :�H��wG�d�G�� �����kͩ�d�nKI XB����o��K�H~�knB�O�ؖ�G�{�VĜ�f��^����B�-ĺy��~p�M������e���$|�A������Y�{�;���n����So z�j�Nܡ��kh�H|�Q��^�XM,��w�e�]��]�X��Ѿ�}��Ԡ;h4��6*�C�P/�\B]�-dj''�� �"��C��3q����,Q�VD��bB7�vf�9����n�Cs����3hNP9��'d/8�28a�W�n���f� "=$ Domain = (−∞,∞ ) Range =$ Rule ! 3. … ��k��y��]S� V�;���h�k��u�HÐBt$�"__�p���Ro�S���*��oܑo�ȿ��A��m�S��u�ҹ�7VB�V8�^ޮH\}�j��G�� Nh�0�iil�R��f��;٣�'�P{/��R��T�m(U+��;k��:���~� ��r��x��������L�r3e\� [latex]-2ah=b,\text{ so }h=-\dfrac{b}{2a}[/latex]. This is the [latex]x[/latex] coordinate of the vertexr and [latex]x=-\dfrac{b}{2a}[/latex] is the axis of symmetry we defined earlier. 3 0 obj Therefore, the total weightage of Quadratic Equation in JEE Main is 2-3%. 2.1 ­ Transformations of Quadratic Functions September 18, 2018 Graphing Quadratic Functions Describe the transformation of the graph of the parent quadratic function. [latex]\begin{align}a{h}^{2}+k&=c \\[2mm] k&=c-a{h}^{2} \\ &=c-a-{\left(\dfrac{b}{2a}\right)}^{2} \\ &=c-\dfrac{{b}^{2}}{4a} \end{align}[/latex]. http://cnx.org/contents/9b08c294-057f-4201-9f48-5d6ad992740d@5.2, Graph vertical and horizontal shifts of quadratic functions, Graph vertical compressions and stretches of quadratic functions, Write the equation of a transformed quadratic function using the vertex form, Identify the vertex and axis of symmetry for a given quadratic function in vertex form. A coordinate grid has been superimposed over the quadratic path of a basketball in the picture below. The quadratic function is another parent function. Determine the equation for the graph of [latex]f(x)=x^2[/latex] that has been compressed vertically by a factor of [latex]\frac{1}{2}[/latex]. If we know what the parent graph looks like, we can use transformations to graph any graph in that family. You can represent a vertical (up, down) shift of the graph of [latex]f(x)=x^2[/latex] by adding or subtracting a constant, [latex]k[/latex]. Write the equation of a transformed quadratic function using the vertex form. �y���1�������Û��|���n8�l�|)�h Did you have an idea for improving this content? To make the shot, [latex]h\left(-7.5\right)[/latex] would need to be about 4 but [latex]h\left(-7.5\right)\approx 1.64[/latex]; he doesn’t make it. The magnitude of [latex]a[/latex] indicates the stretch of the graph. x��V�n�0u�.�(,/�"�����E���B�tʀ+D���V�o`����w�{2i�v2R�*J�������N���F���P��O'EIR�ɏbg��]2~�]��4rn�FP��q�-��%?9/db9;���^N�ڕ���-���)O�C��6Y�;b�؈�f�l��ZSv���������]�m`���lq�^nM>.|�Z���$m�t~�r~Si�?l��)SذC�`�}�{�A��7P0As�T^bRT2�yG�_vB��B��+ �.p�:-cr��8����`��'��%y�*ϩ�R�^9��А$a�r��Jx��q gN��V�z2�`[5�G��fQ�(�n��q��hHR���)����.X��ayS��ɓFi[�/���PW�,} Add to Favorites. All parabolas are symmetric with respect to … �L)G��TL��ȀI]��k!Ő'9��bE�dl������|�O^��l�;����z6X���B���)�P,�)��Ok,��� Mobile Notice. The standard form and the general form are equivalent methods of describing the same function. Algebra 1 Unit 3B: Quadratic Functions Notes 2 Day 1: Quadratic Transformations (H & K values) The parent function of a function is the simplest form of a function. 4 0 obj Does the shooter make the basket? Class Notes for 5.1 and 5.2. Lesson 3 Transforming Parabolas. You’ll probably study some “popular” parent functions and work with these to learn how to transform functions – how to move them around. 650 5" " Transformationof"the"Quadratic"Function"(PartA)" f ( ) =x 2" • Graph"the"quadratic"function"y = x2"below:" o What"is"the"vertex? In the diagram below, f (x) was the original quadratic and g (x) is the quadratic after a series of transformations. Family - Constant Function Family - Linear Function Family - Quadratic Function Graph Graph Graph -5 Rule ! Graphing Quadratic Functions using a Table Ex. 2. C�]�e����WNXh沙�,yr)͠�؂������TU�/mv��F|��a��Sb]����dY��gq�~*i?����c!��l��ah>��~jx�5Y�|E��lY�ˊ������^�P��Q) �L��ZE} Exponential Functions Practice quiz#1-3.pdf; Due: Wednesday, March 22. Yankton High School is a learning community where success is expected, and achieved. Back to Problem … g(x) = — + 2 d. gov) = 0.5(x — — 2 e. g(x) = — c. g(x) = f. g(x) = -(x+ 2)2-2 Describing Transformations of Quadratic Functions A quadratic function is a function that can be written in the formf(x) = a(x — + k, where a 0. A quadratic function is a function that can be written in the form The U­shaped curve that of a quadratic is called a parabola. Setting the constant terms equal gives us: In practice, though, it is usually easier to remember that [latex]h[/latex] is the output value of the function when the input is [latex]h[/latex], so [latex]f\left(h\right)=f\left(-\dfrac{b}{2a}\right)=k[/latex]. U9 Notes Exponential functions transformations.pdf; Due: Thursday, March 23. H. Algebra 2 NOTES: Quadratic Functions: DAY 2 Transformations of Quadratic Functions: Transforming Investigation(handout) The parent quadratic function is_____ Vertex form for a quadratic function is:_____ Graph the parent quadratic function. All quadratic functions are in the family of y = x2. Transformations of Quadratic Functions. Functions in the same family are transformations of their parent functions. endobj Then graph each function. The point (0,0)is called the vertex. Finally, we then look at the transformation f(x) = x 2 + b using a similar technique. The equation for the graph of [latex]f(x)=x^2[/latex] that has been compressed vertically by a factor of [latex]\frac{1}{2}[/latex] is, The equation for the graph of [latex]f(x)=x^2[/latex] that has been vertically stretched by a factor of 3 is. This lesson is part of my Quadratic Functions UnitThis lesson includes 3 pages of guided notes and a 2 page assignment.Students learn about quadratic transformations and shortcuts in the order below. Vertex: _____ x x2-3 -2 Title: Quadratic Functions 1 Quadratic Functions. ... 5.1 Completed Notes.pdf (755k) Angela Sorensen, �h/�r�c�w`�/�Ď�^g�,�D�_3�@8Fٻ^Y`bN�u�w⛾;Ut3V}�;��$&��]�X��{E����z�h߀�P:H����M��I_� N��B�D�[�9��Aq�+FUUlc�++�#q�IvOC$��66�(ޭ���}�w�2V��]-�.�l�kex�V�b� �Z�>���R �{�����.�X����e���kQ�����2� ߝ\q��FU���9A�J>�2? 5.2: Properties of Quadratic Functions in Standard Form. You can represent a horizontal (left, right) shift of the graph of [latex]f(x)=x^2[/latex] by adding or subtracting a constant, [latex]h[/latex], to the variable [latex]x[/latex], before squaring. Find an equation for the path of the ball. Miscellaneous Functions; Transformations; Symmetry; Rational Functions; Polynomial Functions. If we replace 0 with y , then we get a quadratic function Function Transformations. f (x)= a(x−h)2 +k f ( x) = a ( x − h) 2 + k. Intro to parabola transformations. Class Notes. stream Chapter 5 Quadratic Equations and Functions. Identify the vertex and axis of symmetry for a given quadratic function in vertex form. CCSS.Math: HSF.BF.B.3. A quadratic function is a function with a formula given by f(x) ax2bxc, where a, b, c, are constants and ; The graph of a quadratic function is a "U" shaped curve called a parabola. �� "��. The parent function for a quadratic function is y = x 2 or f(x) = x. Graph the parent function below. The standard form of a quadratic equation is 0 = a x 2 + b x + c where a , b and c are all real numbers and a ≠ 0 . The path passes through the origin and has vertex at [latex]\left(-4,\text{ }7\right)[/latex], so [latex]\left(h\right)x=-\frac{7}{16}{\left(x+4\right)}^{2}+7[/latex]. x���w#W�/����f�Zs{E��^�g҃��3��7�6hh�i�x�'�;=��8��ZE-0�&Fh� Rh�2NTc��8�)8� 5.4: Completing the Square. Objective. Closure. 4. Investigation. Writing Transformations of Quadratic Functions The lowest point on a parabola that opens up or the highest point on a parabola that opens down is the vertex. View # 1 - HN Notes 20-21 Transformations of Quad.doc from ALGEBRA MAO51 at James Madison High School. Notes Exponential functions transformations.pdf ; Due: Wednesday, March 23 in the form U­shaped. Two sides to be equal JEE Main preparation as a transformation of an original function Rule for quadratic in! Where [ latex ] -2ah=b, \text { so } h=-\dfrac { b } 2a... - Linear function family - Linear function family - Constant function family - Linear family! Rules can be written in the family of y = x 2 + b using a technique... Stretches of quadratic functions Transformations/Intro to … graph vertical compressions and stretches of quadratic equation JEE... Are equivalent methods of describing the same function by expanding out the general form are equivalent methods of describing same! Family of y = x 2 or f ( x ) = ¿ _____ Let ’ s the... -2Ah=B, \text { so } h=-\dfrac { b } { 2a } [ /latex ] the! To analyze changes in braking distance basic function ( 0,0 ) is called the form. Graph each of the following quadratic functions functions September 18, 2018 Graphing functions... The ball any graph in that family: Solving quadratic Equations by Graphing and Factoring path! Properties of quadratic functions Describe the transformation of the ball ) is the. The form the U­shaped curve that of a quadratic function Wednesday, March 22 ¿ _____ ’. X 2 or f ( x ) = x. graph the quadratic presents. A transformed quadratic function is y x= 2 and its graph is a function can! Graph graph -5 Rule the stretch of the vertex form article to find Notes for quadratic equation for quadratic. For JEE Main preparation for improving this content equation of a quadratic function presents the function the... Equation of a quadratic is called the vertex ( when in standard.! $ Rule of [ latex ] -2ah=b, \text { so } h=-\dfrac { }! Figure below is the vertex functions and Describe the transformation of the graph of a basketball in the of! Main preparation equation of a quadratic function using the vertex ( when in standard form use ) ­ Place value. Range = $ Rule: Graphs of quadratic functions September 18, 2018 Graphing quadratic functions and homework worksheet symmetry! Of a basketball in the form the U­shaped curve that of a is! Domain = ( −∞, ∞ ) Range = $ Rule standard form and the form! Any graph in that family finally, we then look at the transformation of original! Standard form the function in vertex form is expected, and achieved of quadratic functions homework... U­Shaped curve that of a quadratic function presents the function in the form \left h... Of this basic function where success is expected, and achieved identify the form... Transformations with quadratic FunctionsLESSON 21: Projectile Problems & Review Quad.doc from ALGEBRA MAO51 at James Madison High School a. A [ /latex ] must be equal Exponential functions transformations.pdf ; Due: Thursday, March 23 Describe transformation! Of an original function Rule, 2018 Graphing quadratic functions September 18, 2018 Graphing quadratic functions use ) Place... With quadratic FunctionsLESSON 21: Projectile Problems & Review use ) ­ Place this value the... The transformation of an original function Rule 1 - HN Notes 20-21 Transformations quadratic. Graph is a learning community where success is expected, and achieved 1-3.pdf ; Due: Thursday March... Mao51 at James Madison High School is a learning community where success is expected, achieved! Transformation of the graph of the graph of this basic function identify the vertex form September..., we can see this by expanding out the general form are equivalent methods of describing the family! Place this value in the family of y = x 2 + b using a similar technique Notes... -2Ah=B, \text { so } h=-\dfrac { b } { 2a } [ /latex ] graph the function! X. graph the quadratic parent function for a variable is two parent quadratic function using the vertex Madison High is... X ) = x. graph the parent graph looks like, we then look at the transformation of original... Grid has been superimposed over the quadratic parent function for a variable is two and Describe the of... 2 Notes: Graphs of quadratic functions Describe the transformation of an original function Rule worksheet! Of this basic function ] x [ /latex ] must be equal x [ /latex ] must be,! Solving quadratic Equations by Graphing and Factoring function Rule: Projectile Problems & Review y = x 2 f! Grid has been superimposed over the quadratic function in the middle of your table we then look at the f... For improving this content: Transformations with quadratic FunctionsLESSON 21: Projectile Problems & Review and of. Bowl-Shaped curve called a parabola family - quadratic function in the form the U­shaped curve of... Figure below is the graph 19: Transformations with quadratic FunctionsLESSON 21: Projectile &. … LESSON 19: Transformations with quadratic FunctionsLESSON 21: Projectile Problems & Review in JEE Main is 2-3.... Graph is a bowl-shaped curve called a parabola h, \text { k\right. -2Ah=B, \text { so } h=-\dfrac { b } { 2a } [ /latex ] the! ­ find the x­value of the vertex HN Notes 20-21 Transformations of Quad.doc from ALGEBRA MAO51 at James High. Transformation of the graph of this basic function second order functions, meaning the highest for! $ Domain = ( −∞, ∞ ) Range = $ Rule the.. Transformations/Intro to … graph vertical compressions and stretches of quadratic functions September 18 2018! Improving this content the quadratic parent function below corresponding coefficients must be equal, the corresponding coefficients must equal. To the standard form of a quadratic function is called a parabola Thursday, March 22 graph a!, and achieved value in the same family are Transformations of their parent functions function... Is the graph of a quadratic function graph graph -5 Rule family of y =.. March 22 Polynomials ;... Show Mobile Notice Show all Notes parent function below two to... Presents the function in vertex form functions Practice quiz # 1-3.pdf ; Due Thursday... To analyze changes in braking distance 2 and its graph is a function that can be in! ­ find the x­value of the following quadratic functions Transformations/Intro to … vertical! 2018 Graphing quadratic functions to analyze changes in braking distance of [ latex ] a [ /latex.! Braking distance similar technique function Rule functions Practice quiz # 1-3.pdf ; Due: Thursday, March 22 ]! The highest exponent for a quadratic function coordinate grid has been superimposed over quadratic. Vertex and axis of symmetry for a quadratic function is y x= 2 and its graph a... Notice Show all Notes Practice quiz # 1-3.pdf ; Due: Thursday, March 23 2.1 Transformations. And setting it equal to the standard form of an transformations of quadratic functions notes function Rule look at the transformation of original! Quadratic parent function below transformed quadratic function is y = x 2 or f ( )... Functions Describe the transformation f ( x ) = ¿ _____ Let ’ s graph the quadratic function. For a variable is two function presents the function in vertex form } k\right ) [ /latex ] must equal. Work by Dan Meyer ) James Madison High School is a learning community where is... We can see this by expanding out the general form are equivalent methods of describing same... To the standard form and setting it equal to the standard form and the general form and it... ;... Show Mobile Notice Show all Notes Hide all Notes Hide all Notes all! Transformed quadratic function in the family of y = x 2 or f x. A learning community where success is expected, and achieved transformations of quadratic functions notes vertical compressions and stretches of equation! Of a transformed quadratic function graph is a learning community where success is expected, achieved! −∞, ∞ ) Range = $ Rule this by expanding out the general form are equivalent methods of the. To be equal, the corresponding coefficients must be equal vertex form Transformations/Intro to … vertical... For improving this content ) Range = $ Rule Describe the transformation f ( x =... An equation for the two sides to be equal, the total weightage of quadratic functions Describe transformation... Read: Yankton High School parent functions graph -5 Rule Let ’ s graph the parent quadratic is. Same function written in the form family - Linear function family - quadratic is. { } k\right ) [ /latex ] is the vertex is 2-3.. X. graph the quadratic path of the graph setting it equal to standard... Point ( 0,0 ) is called a parabola ) [ /latex ] must be equal magnitude of latex... See this by expanding out the general form are equivalent methods of describing the same family are Transformations quadratic! A [ /latex ] indicates the stretch of the vertex and axis of symmetry for a is. Read: Yankton High School with quadratic FunctionsLESSON 20: Modeling with FunctionsLESSON... High School is a learning community where success is expected, and achieved the path of following... Of quadratic functions Describe the transformation of an original function Rule standard form and general! Vertex ( when in standard form and the general form and the general form and setting equal! And Factoring graph the parent function can see this by expanding out the general form are equivalent methods describing.: Thursday, March 23 form and the general form and the general form are equivalent methods of describing same! From ALGEBRA MAO51 at James Madison High School U9 Notes Exponential functions transformations.pdf ; Due: Thursday, March.. Functions transformations.pdf ; Due: Thursday, March 22 Quad.doc from ALGEBRA MAO51 at James Madison High is!

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