Solving Quadratic Equations

Factoring

100

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

Quadratic Facts

100

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

x-intercepts

200

Which part of a quadratic equation indicates if the parabola opens up or down?

a

the coefficient of x²

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 is the quadratic equation in standard form?

y=ax²+bx+c

500

How do we know which method to use to solve quadratic equations? 

Think factoring vs. quadratic formula

You can always use the quadratic formula but you can't always use factoring.

Features of Parabolas

100

This is the point where a quadratic function crosses the x-axis

x-intercept, solution, zero, root

200

This point is the center of a parabola and can be a maximum or minimum, depending on the direction of the parabola.

Vertex

300

This line crosses the vertex of a parabola and divides the parabola in half.

Axis of Symmetry

400

The __________ form of quadratic equations is useful for finding the vertex.

Vertex Form

500

Draw a sketch of a parabola and label the following features:

 x-intercepts, vertex, minimum, axis of symmetry

Answers will vary.

Quadratic Formula

100

What is the quadratic formula?

x = -b +- sqrt(b² - 4ac) /(2a)

200

Identify a, b and c in the following equation: 

x² + 6x + 5 = 0

a = 1; b = 6; c = 5

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

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:

-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