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.

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

Example) Convert f(x) = -(x + 2)2 into standard form.

Transformation in Function NotationTransformations 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 + 4h(x) = 3(-x – 1)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)

j(x) = 3((x – 2) – 1)2 + 4j(x) = 3(x – 3)2 – 4

k(x) = 3((2x) – 1)2 + 4 + 2k(x) = 3(2x – 1)2 + 6

m(x) = (3((x – 1) – 1)2 + 4) + 1m(x) = ( 3(x – 2)2+ 4) + 1m(x) = (x – 2)2 – 2 + 1m(x) = (x – 2)2 – 1

HW pg. 320

#’s 14, 29, 30, 32, 43, 44, 51, 52