Quadratics

y = x 2

Flips up because positive

value

Doesn’t move left or right on x axis. Stays at 0

Doesn’t move up or

down y axis. Stays

at 0

This is the “parent”.

y = 1/2 x2

Flips up because negative

value

Doesn’t move left or right.

Stays at 0

Doesn’t move up or

down. Stays at 0

Makes parabola

wider

y = -4x2 + 2

Flips down because negative

value

Doesn’t move left or right.

Stays at 0

Moves up 2 on y axis

Makes parabola skinnier

y = 1/2 (x+3)2

Flips up because negative

value

Moves left 3 on x axis Doesn’t

move up or down.

Stays at 0

Makes parabola

wider

y = (x – 4)2 + 5

Flips up because positive

value

Moves right 4 on x

axis

Moves up 5 on y axis

y = -(x + 2)2 - 5

Flips down because negative

value

Moves left 2 on x axis

Moves down 5 on

y axis

y = - 3(x – 4)2 + 9

y = x2 – 7x + 12

y = (x – 3)(x + 6)

Quadratic Family

Moves parent right 4 and up 5.

This is the NEW vertex.

x intercept:

y intercept:

vertex:

D:

R:

none

(0,21)

(4,5)

{ y : y > 5}

y = x2 – 7x + 12

HOW DO YOU FIND THE X

INTERCEPTS?Set y = 0 0 = - 3(x – 4)2 + 9

Minus 9 from both sides.-9 = - 3(x – 4)2 Divide by -3 3 = (x – 4)2

Square Root both sides 1.73 = x – 4

-1.73 = x - 4Solve.(5.73, 0) and (2.27, 0)

HOW DO YOU FIND THE X

INTERCEPTS?Set y = 0 Factor

OR

Quadratic Formula

HOW DO YOU FIND THE VERTEX?

-b2a

This gives you the X

COORDINATE of the vertex. To

find the y, substitute this x into the original and evaluate.

OR You Could

Use the Midpoint of the x

intercepts.

HOW DO YOU FIND THE VERTEX?

Find the midpoint of the x intercepts. Then substitute that x into the original to find it’s

y coordinate.

y = (x + 8)(x - 2)

HOW DO YOU FIND THE X

INTERCEPTS?Set each factor equal to 0 and solve. (Take the opposite of them.)

(-8,0) and (2,0)

6th hour ends. They need rest of this and FF1

y = (3x + 2)(5x - 2)

Quadratic Family

x intercept:

y intercept:

vertex:

D:

R:

(-2/3, 0) (2/5, 0)

(0,-4)

(-2/15, -4.27)

{ y : y > -4.27}

y = x2 – 7x + 12

Quadratic Family

x intercept:

y intercept:

vertex:

D:

R:

(4, 0) (3, 0)

(0,12)

(3.5, -.25 )

{ y : y > -.25}

y = x2 + 6x + 1

Quadratic Family

x intercept:

y intercept:

vertex:

D:

R:

NONE

(0,1)

{ y : y > -8}

Because there are NO x intercepts

YOU MUST USE –b/2a to find the

VERTEX!!!(-3, -8)

x2 – 9

4x2 – 49

Factor(2x – 7)(2x + 7)

16x2 – 46x + 49

Factor(4x – 7)(4x - 7)

x2 – 7x - 18

Factor(x + 9)(x - 2)

12x4 – 3x3

Factor(3x3)(4x + 1)

(x + 10)(x - 2)

QUICK FOILx2 + 8x - 20

(x - 3)(x - 2)

QUICK FOILx2 - 5x + 6

(x – 5)2

QUICK FOILx2 - 12x + 36

(3x + 2)2

QUICK FOIL9x2 + 12x + 4