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 completing square. x² - 6x + 5 = 0

x = 5 x = 1

400

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

x = 9 x = -3

500

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

x = -1/2 x = 3

Quadratic Facts

100

What is the discriminant of a quadratic equation, and how does it help determine the nature of the solutions?

delta 

200

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

No solution, One solution or Two solutions

300

Solve the following quadratic equation by completing the square: x² + 6x + 8 = 0.

x=2 or x=4

400

Why is the quadratic formula useful for solving quadratic equations?

We can ALWAYS use the quadratic formula, but we cannot always factor.

500

 Convert the quadratic equation y = 2(x - 3)² + 5 into standard form (ax²+ bx + c = 0). What are the values of a, b, and c?

2x²-12x+23

a=2,b=-12,c=2

Quadratic Formula

100

What is the quadratic formula?

x= +-b √( b² - 4ac) /2a

200

When solving a quadratic equation, what does it mean if the discriminant is positive, zero, or negative?

positive:2 solution

zero:one solution

negative: no solution

300

Identify a, b and c in the following equation: 

x² - 9x + 20 = 9

a = 1; b = -9; c = 11

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's the best method?

100

Identify a, b and c in the following equation: 

x² + 6x + 5 = 0

a = 1; b = 6; c = 5

200

Find the best method for solving the quadratic equation below:

-x²-4 = 0

Factoring

300

Find the best method for solving the quadratic equation below:

5x²+2x-2 = 0

Quadratic Formula

400

Find the best method for solving the quadratic equation below:

x²-7x+5 = 0

Quadratic Formula

500

True or false?

Using the quadratic formula and factoring will give you different results.

False

Graph Openings

100

Does the graph of this equation open up or down?

 y = (x+2)(x-1)

Opens Up

200

Does the graph of this equation open up or down? 

y = -4(x-2)² + 2

Open Down

300

Does the graph of this equation open up or down? 

y = 2(x-1)² - 6

Open Up

400

Does the graph of this equation open up or down? 

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

Open Up

500

Does the graph of this equation open up or down?

 y = -3(x+4)² - 2

Open down