Algebra 2 MCR Unit 2-Quadratic Functions

Translations: f(x+h)

Left horizontally “h” units

Translations: f(x-h)

Right horizontally “h” units

Translations: f(x)+k

Up “k” units

Translations: f(x)-k

Down '“k” units

Stretches & Shrinks: a*f(x). If |a|>1, then…

STRETCH vertically by a factor of a.

Stretches & Shrinks: a*f(x). |a|<1, then…

SHRINK vertically, (fraction)

Reflections: -f(x)

Reflection over x - axis

Absolute Value

DISTANCE away from 0.

Absolute Value Equation

y=|x|

Vertex

(0,0)

Axis of Symmetry

X=0

Translation Form of an Absolute Value Function

f(x)=a|x-h|+k

Vertex in f(x)=a|x-h|+k

(h,k)

Slope of Right side in f(x)=a|x-h|+k

“a” (stretch or shrink)

Quadratic Function shape & name

• U shaped

• Parabola

(Quadratic Function) Standard Form

ax² + bx+c

ax² + bx+c: What does “a” do?

In ax² + bx+c, “a” determines shape

AOS equation in Standard Form

-b/2a

Y intercept in Standard Form

C

(Quadratic Function) Vertex Form:

a(x-h)² +k

a(x-h)² +k: What does “a” do?

in a(x-h)² +k, “a” determines shape

AOS equation in Vertex Form

x-h

Vertex equation in Vertex form

Vertex = (h,k)

(Quadratic Function) Intercept Form:

a(x-p)(x-q)

Intercept Form: What “a” determines

In a(x-p)(x-q), “a” determines shape

AOS Equation in Intercept form

p+q/2

X-intercepts in Intercept Form

p,q