Quadratics

Graphing to Solve

100

Which variable is equal to 0 to find the zero of a function?

y = 0

200

What is an x - intercept? 

Where the graph crosses the x-axis, and when y = 0

300

What is the zero of a graph? 

Any x - intercept(s)

400

What is the formula to find the axis of symmetry? 

x = -b/(2a)

500

How do you find the vertex? 

Find x = -b/(2a), then plug in the value to find y. 

Find the Zeros

100

Find the zeros of the function.

(x + 2)(x + 1) = 0

x = -2, -1

200

Find the zeros of the function.

x(x - 2) = 0

x = 0, 2

300

Find the zeros of the function.

(2x - 1)(x + 3) = 0

x = 1/2, -3

400

Find the zeros of the function.

4(x - 5)(4x + 3) = 0

x = 5, -3/4

500

Find the zeros of the function.

(5x - 2)(3x + 1) = 0

x = 2/5, -1/3

Factoring with a Leading Coefficient of 1

100

Factor.

x² + 6x + 8

(x + 2)(x + 4)

200

Factor.

x² + 10x + 9

(x + 1)(x + 9)

300

Factor.

x² - 8x + 12

(x - 2)(x - 6)

400

Solve by factoring.

x² - 5x - 14 = 0

x = 7, -2

500

Solve by factoring.

x² + 5x - 24 = 0

x = -8, 3

Factoring with a Different Leading Coefficient

100

Factor.

3x² + 13x + 12

(3x + 4)(x + 3)

200

Factor.

2x² - 5x + 2

(2x - 1)(x - 2)

300

Factor.

2x² - 3x - 5

(2x - 5)(x + 1)

400

Solve by factoring.

8x² - 11x + 3 = 0

x = 3/8, 1

500

Solve by factoring.

2x² + 9x = -9 

x = -3, -3/2

Rewriting Radicals

100

Simplify.

√36

6

200

Simplify.

√18

3√2

300

Simplify.

√12x⁴

2x²√3

400

Simplify.

√8x⁵

2x²√2x

500

Simplify.

√75x³y⁸

5xy⁴√3x