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5-1 Transforming Quadratics in Function Notation and Converting to Standard Form

5-1 Transforming Quadratics in Function Notation and Converting to Standard Form. A function written in vertex form, f(x) = a(x – h) 2 + k, can be converted to standard form, f(x) = ax 2 + bx + c by using PEMDAS. Example) Convert f(x) = ( x + 2) 2 – 1 into standard form. .

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5-1 Transforming Quadratics in Function Notation and Converting to Standard Form

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  1. 5-1 Transforming Quadratics in Function Notation and Converting to Standard Form A function written in vertex form, f(x) = a(x – h)2 + k, can be converted to standard form, f(x) = ax2 + bx + c by using PEMDAS. Example) Convert f(x) = (x + 2)2 – 1 into standard form.

  2. Example) Convert f(x) = 3(x – 1)2+ 4 into standard form. Example) Convert f(x) = -(x + 2)2 into standard form.

  3. Transformation in Function Notation Transformations of functions can be written as a substitution into f(x). This is called function notation. Example) Given f(x) = 3(x – 1)2 + 4, a) if g(x) = -f(x) determine the equation for g(x) b) if h(x) = f(-x) determine the equation of h(x) g(x) = -(3(x – 1)2 + 4) g(x) = -3(x – 1)2 – 4 h(x) = 3((-x) – 1))2+ 4 h(x) = 3(-x – 1)2+4

  4. j(x) = 3((x – 2) – 1)2 + 4 j(x) = 3(x – 3)2 – 4 c) if j(x) = f(x – 2) determine the equation of j(x) d) if k(x) = f(2x) + 2 determine the equation of k(x) e) if m(x) = f(x – 1) + 1 determine m(x) k(x) = 3((2x) – 1)2 + 4 + 2 k(x) = 3(2x – 1)2+6 m(x) = (3((x – 1) – 1)2 + 4) + 1 m(x) = ( 3(x – 2)2+ 4) + 1 m(x) = (x – 2)2 – 2 + 1 m(x) = (x – 2)2 – 1

  5. HW pg. 320 #’s 14, 29, 30, 32, 43, 44, 51, 52

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