Solving Quadratic Equations

Factoring

100

Solve the following quadratic equation. 

(x - 7)(x + 2) = 0

x = 7 x = -2

200

Solve the following quadratic equation. 

x²+3x+2 = 0

x = -2 x = -1

300

Solve the following quadratic equation. 

x² - 6x + 5 = 0

x = 5 x = 1

400

Solve the following quadratic equation. 

x² - 6x - 27 = 0

x = 9 x = -3

500

What are the solutions to the equation:

 2x² - 5x - 3 = 0

x = -1/2 x = 3

Square Roots

100

What are the solutions to the following equation? 

 x² = 4

x = 2 x = -2

200

What are the solutions to this equation?

 4x² - 16 = 240

+8 or -8

300

What are the solutions to this equation? 

4x² = 400

x = 10 x = -10

400

What are the solutions to this equation?

 x² -9 = -8

1 or -1

500

What are the solutions to this equation?

5(x-2)² + 3 = 128

x = 7    x = -3

Writing Equations

100

Write a quadratic equation of a parabola with intercepts (2,0) and (3,0), and a equals 4, in factored form.

y = 4(x-2)(x-3)

200

Write a quadratic equation of a parabola with intercepts (-8,0) and (8,0), and a equals -3, in factored form.

y = -3(x+8)(x-8)

300

Write a quadratic equation of a parabola with vertex (-5,12), and a equals -2, in vertex form

y = -2(x+5)² + 12

400

Write a quadratic equation of a parabola with intercepts (1,0) and (6,0), and an extra point (2,4).

y = -(x-1)(x-6)

500

Write a quadratic equation of a parabola with intercepts (-3,0) and (5,0), and an extra point (1,32) in factored form.

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

Quadratic Formula

100

What is the quadratic formula?

x = -b +- sqrt(b² - 4ac) /(2a)

200

Solve the following quadratic equation by using the quadratic formula: x² + 6x + 5 = 0

x = -1 x = -5

300

Solve the following quadratic equation by using the quadratic formula: x² - 9x + 20 = 0

x = 5 x = 4

400

Solve the following quadratic equation by using the quadratic formula: 2x² + 9x + 4 = 0

x = -1/2 x = -4

500

Solve the following quadratic equation by using the quadratic formula: 4x² - 17x = 15

x = 5 x = -3/4

Function Notation

100

f(x)=-x²+8x-15

Find f(0)

-15

200

f(x)=x²-2x

Find f(2)

0

300

f(x)=5x²+2x-2

Find f(1)

5

400

The function, h(x)=2x²+4x+16 could be used to represent the height of a ball, h, in feet thrown after x seconds.

Find h(4) and interpret its meaning.

After 4 seconds, the ball reached a height of 64 feet.

500

The function, h(x)=3x²+5x+21 could be used to represent the height of a ball, h, in feet thrown after x seconds.

Find h(2) and interpret its meaning.

After 2 seconds, the ball reached a height of 43 feet.