Applying Quadratic Models

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f(x)=a(x-r)(x-s)

roots (x intercepts) x=r and x=s

axis of symmetry = (r+s)/2

vertex= ( (r+s)/2 , y )

Applying Quadratic Models

f(x)=a(x-h)^2+k

EXPAND

f(x)=ax^2+bx+c

c is the "y intercept"

the vertex is always (h,k)

"K"

the parabola moves "k" units up or down

"h"

value of "h" is the axis of symmetry

the parabola moves "h" units left or right.

"h" is negative, parabola moves rigt

"h" is positive, parabola moves left

Changing Standard Form to Vertex Form

COMPLETING THE SQUARE

Subtopic

"a" in standard, factored and vertex form

When a is negative, parabola opens downwards

a<0

Parabola is reflected across the x axis

When "a" is negative and

When "a" is negative and a>1 parabola is stretched then reflected

red parabola is y=-x^2

When a is positive, parabola opens upwards

0

Parabola is compressed vertically by a factor of "a"

the greater the value of "a" the more compressed

red parabola is y=0.5x^2

a>1

Parabola is stretched vertically by a factor of "a"

the greater the value of "a" the more stretched

red parabola is y=2x^2

blue parabola is y=x^2