Solving Quadratic Equations

Quadratic Facts

100

When solving quadratic equations, we are trying to find what feature of the parabola?

x-intercepts

200

What are the three different types of solutions we can have when solving quadratics

No solution, One solution or Two solutions

300

How do we know a quadratic function does not have solutions when looking at a graph?

It does not touch the x-axis

400

What does ax^2+bx equal when there are no solutions?

What is a negative number?

500

What does ax^2+bx equal when there is one solution?

What is zero?

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

Completing the Square

100

Solve the quadratic equation by completing the square.

x^2+14x-38=0

What is 

-7 +-sqrt87

200

Solve the quadratic equation by completing the square.  

x^2-12x+23=0

What is 

6+-sqrt13

300

Solving the quadratic equation by completing the square.  

x^2-4x-91=7

What is 

2 +-sqrt102

400

Solve the quadratic equation by completing the square. 

8x^2+16x=42

What is 

3/2 and -7/2

500

Solve the quadratic equation by completing the square.

3x^2=-4+8x

 

What is 

2 and 2/3