Quadratics

Standard to Vertex Form

100

y = x² - 4x - 7

y = (x-2)² - 11

200

x² + 9x + 1

y = (x+4.5)² - 19.25

300

give us the vertex and vertex form 

x² - 8x +15

(x-4)² - 1

(4, -1)

400

2x² + 12x +13

2(x+3)² - 5

500

y = -5x² + 80x - 313

y = -5(x-8)² + 7

Axis of Symmetry and Vertex (with Formula)

100

Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (�,�)(x,y) point.

y =-x² - 16x - 57

(-8,3)

200

x² - 2x + 4

(1,3)

300

-2x² + 8x

(2,8)

400

2x² + 12x + 36 

(-3,18)

500

4x² + 48x + 160

x = -6

Solving Quadratics by Factoring

100

x² - 10x - 4 = -2x - 4

x=0

x=8

200

x² - 10x - 6 = -2x -6

x=0

x=8

300

x² - 6x - 64 = -6x

x={8,-8}

400

x²-9x-20=-2x-2

x={-2,9}

500

A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out the maximum amount of profit the company can make, to the nearest dollar.

-4x²+141x-703

y=$540→Max profit

Factor Trinomials

100

x²−10x+16

(x-2)(x-8)

200

x²+5x-6

(x-1)(x+6)

300

3x²+20x+25

(3x+5)(x+5)

400

5x²+27x+28

(5x+7)(x+4)

500

5x²−18x+9

(5x-3)(x-3)

Select Form to Find Quadratic Feature

100

Find the y intercept of 2x²−20x+42

(0,42)

200

Find the zeros of 3(x+1)(x+7)

x=-1

x=-7

300

Find the x intercept 

3(x−5)(x+1)

x=5

x=−1

400

Find the vertex of

2(x−2)²−50

(2,-50)

500

Find the Vertex

3x²+12x−36

(-6,0)