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

Square Roots

100

Solve the following quadratic equation by using square roots: x² = 4

x = 2 x = -2

200

Solve the following quadratic equation by using square roots: x² = 121

+11 or -11

300

Solve the following quadratic equation by using square roots: 4x² = 400

x = 10 x = -10

400

Solve the following quadratic equation by using square roots: x² -9 = -8

1 or -1

500

Solve the following quadratic equation by using square roots: 5x² + 3 = 128

x = 5 x = -5

Completing the Square

100

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

x = -2 x = -4

200

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

x = 1 x = 5

300

What step is different in the process of completing the square when a>1?  

Before finding the term to complete the square, you must divide each term by a.  

400

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

x = -2 x = -8

500

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

x = 5 x = -1

Quadratic HodgePodge

100

What are the steps for solving quadratics using the square root method?  

It must be a binomial with only an x squared term and a constant.  Isolate the x squared term.  Take the square root of both sides.  

200

The length of a rectangle is 1 meter less than its width.  The area of the rectangle is 42 square meters.  What are the dimensions of the rectangle?  

7 m by 6 m

300

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

x = 5 x = 4

400

The dimensions of a rectangle can be expressed as x+3 and x-8.  If the area of the rectangle is 60 square inches, find the value of x.  

x= 12 inches

500

Find the vertex and axis of symmetry of this quadratic equation: 2x² - 12x+8= 0

Vertex: (3,-10)

AOS: x=3

Find The Vertex

100

Find the vertex of f(x)=-x²+8x-15

(4,1)

200

Find the vertex of f(x)=x²-2x

(1,-1)

300

Find the vertex of f(x)=5x²+2x-2

(-1/5,-11/5)

400

f(x)=-x²-4x

(-2,4)

500

Find the vertex of x=5y²+4y+3

(11/5,-2/5)