Investigating Monomials (pp. 1 of 4)

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Investigating Transformations on Quadratic Functions (pp. 3 of 3) Summarize observations in the table below. Algebra 2 HS Mathematics Unit: 06 Lesson: 02 Function Effect Domain/Range 2 y x Parent Function D: All real numbers R: y 0 Tell how the functions below are different from the parent function. 2 y x y x 2 4 y x 2 4 y 2 ( x 4) 2 y ( x 4) 2 y 2x y 1 2 2 x ©2010, TESCCC 08/01/10 page 12 of 40
Characteristics of Quadratic Functions (pp. 1 of 5) Algebra 2 HS Mathematics Unit: 06 Lesson: 02 Here are the two forms in which quadratic functions can be written: Vertex Form: 2 y a( x h) k General (Standard) Form: 2 y ax bx c In these equations, a, b, and c, h, and k represent constants, but a cannot equal zero. Why must we say a 0 ? Comparison of Characteristics Characteristic vertex axis of symmetry Standard Form 2 y ax bx c ( b 2 a , ?) b Plug x = into the 2a equation to find y b x 2a y-intercept (0, c) point symmetric to y-intercept x-intercept(s) Vertex Form 2 y a( x h) k (h, k) x = h (0, ?) Plug x = 0 into the equation to find y The y-intercept (and other points) can be reflected across the axis of symmetry to find other points on the graph of the function. These points can be read from the graph or table. When in doubt, use the calculator’s CALC 2: zero command (2 nd , TRACE). The two forms of quadratic equations provide information about the function’s graph in different ways. However, some things are the same, regardless of which form you use. Find each characteristic for the functions described. 2 Characteristic y x 2x 3 y ( x 1) 2 4 vertex axis of symmetry y-intercept symmetric point to y-intercept x-intercept(s) Compare with the results from the handout: Investigating Characteristics of Quadratic Functions. ©2010, TESCCC 08/01/10 page 32 of 40
Page 1 and 2: Investigating Monomials (pp. 1 of 4
Page 3 and 4: Investigating Monomials (pp. 3 of 4
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Investigating Monomials (pp. 1 of 4)

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