Unit 7 Quadratics! Section 9.4: Transforming Quadratic Functions

Guided Notes The value of a in a quadratic function does not just determine the direction a parabola opens, but also the width of the parabola!

Value of a Shape of parabola If 𝑎 > 1

If 𝑎 < 1

If 𝑎 is +

If 𝑎 is -

Shape gets wider

Shape gets narrower

Opens up

Opens down

Comparing Widths of Parabolas: Order the functions from the narrowest graph to the widest

• 𝑓 𝑥 = −2𝑥!, 𝑔 𝑥 = !!𝑥!, ℎ 𝑥 = 4𝑥!

𝑓(𝑥): |𝑎| = |−2| = 2

𝑔(𝑥): |𝑎| = !13! =

13

ℎ(𝑥) = |𝑎| = |4| = 4Narrowtowide(smallesttobiggest):𝑔(𝑥) → 𝑓(𝑥) → ℎ(𝑥)

Unit 7 Quadratics! Section 9.4: Transforming Quadratic Functions

Guided Notes Vertical Translations of a Parabola (shifting the graph up or down):

Compare each graph with the graph of 𝑓 𝑥 = 𝑥!

• 𝑔 𝑥 = − !!𝑥! + 2

• ℎ 𝑥 = 2𝑥! − 3

The graph of the function 𝑓(𝑥) = 𝑥! + 𝑐 is the graph of 𝑓(𝑥) = 𝑥! translated vertically. If 𝑐 > 0, the graph of 𝑓(𝑥) = 𝑥! is translated c units up If 𝑐 < 0, the graph of 𝑓(𝑥) = 𝑥! is translated c units down

The graph is flipped downward because a is negative. The graph is narrower because 𝑎 < 1 The graph is shifted up 2 units because of the +2

The graph is wider because 𝑎 > 1 The graph is shifted down 3 units because of the -3