Solving Quadratic Equations

Factoring

100

Use the Zero Product Property to solve the following quadratic equation. (x - 7)(x + 2) = 0

x = 7 x = -2

200

Solve the following quadratic equation by factoring. x²+3x+2 = 0

x = -2 x = -1

300

Solve the following quadratic equation by factoring. x² - 6x + 5 = 0

x = 5 x = 1

400

Solve the following quadratic equation by factoring. x² - 6x - 27 = 0

x = 9 x = -3

500

Solve the following quadratic equation by factoring. 2x² - 5x - 3 = 0

x = -1/2 x = 3

Graphing

100

Solve the following quadratic equation by graphing: x² + 6x = -8

x = -2 x = -4

200

Solve the following quadratic equation by graphing: x² - 6x = -5

x = 1 x = 5

300

Solve the following quadratic equation by graphing: x² - 2x - 24 = 0

x = -4 x = 6

400

Solve the following quadratic equation by graphing: x² + 10x +16 = 0

x = -2 x = -8

500

Solve the following quadratic equation by graphing: 2x² - 8x = 10

x = 5 x = -1

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 = 0

x = 5 x = -3/4

What are the Factors

100

If the graph has solutions of x=3 and x=-3, what are the factors?

(x+3)(x-3)

200

If the quadratic has solutions of x=5 and x=-2, what are the factors?

(x-5)(x+2)

300

What is the equation of a quadratic in factored form if it has x-intercepts of (5,0) and (-6,0)?

y=(x-5)(x+6)

400

What is the equation of a quadratic in factored form if the quadratic has one solution of x=8?

y=(x-8)²

500

What is an equation of a quadratic in factored form if it has roots of 2/3 and 4

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

Mystery

100

What are the three other names for solutions to Quadratics?

Roots, Zeros, and x-intercepts

200

What mathematical constant represents the ratio between a circle’s circumference and its diameter?

Pi

300

How many real solutions can quadratic equations have?

0, 1, or 2

400

What is the quotient of 8x⁴ and 2x?

4x³

500

What is standard form of a quadratic?

y= ax² + bx + c