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 

or x = { 7, -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

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 real solution (Imaginary), 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  or pass through the x-axis

400

Why is the quadratic formula useful for solving quadratic equations?

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

500

How do we know a quadratic function does not have a real number solution when using the quadratic formula?

The discriminant will be negative. (i.e. the number under the square root)

Linera Inequalities in One Variable

100

Solve the inequality.

5x − 8 > 17

x > 5

200

I'm thinking of an integer. It is greater than 4. It is less than or equal to 8. It is an even number. What number am I thinking of?

6

300

If x > 5x, must x + 10 > 15x + 10 ?

True

400

Which inequality has no solution? 

A. x + 3 > x + 1

B. 5x − 2 > 5x + 7

C. 2x < 2x + 5

D. 7x ≤ 7x

B

500

Three students make these claims about the same counting number.

• Amy: x > 5
• Ben: x < 9
• Chloe: x = 8

Exactly two students are correct.

What is x?

x = 7

Quadratic Formula

100

Identify a, b and c in the following equation: 

x² + 6x + 5 = 0

a = 1; b = 6; c = 5

200

Identify a, b and c in the following equation: 

x² - 9x + 20 = 9

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

300

True or false?

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

False

400

What is the quadratic formula?

x=(-b +- sqrt(b^2-4ac))/(2a)

500

What is the first step for solving an equation using the quadratic formula?

Make sure the equation is in standard form. Then, find a,b and c and evaluate the discriminant.

Random!

100

Find the best method for solving the quadratic equation below:

x²+6x+9 = 0

Factoring

200

Find the best method for solving the quadratic equation below:

5x²+2x-2 = 0

Quadratic Formula

300

What is my last name?

Li

400

What is my favourite colour?

Navy blue

500

How old are Lisa and Amelie?

Lisa is 12 and Amelie is 15.