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?

There will be a negative number under the square root.

Features of Parabolas

100

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

y-intercept

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 into 2 equal halves.

Axis of Symmetry

400

The __________ form of quadratic equations is useful for finding the x-intercepts.

Factored

500

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

y-intercept, x-intercepts, vertex, minimum, axis of symmetry

Answers will vary.

Quadratic Formula

100

What is the quadratic formula?

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

-b +/- sqrt(b² - 4ac) /2a

-9 +/- sqrt(81 - 4(2)(4) /2(2)

-9 +/- sqrt(81 - 32) /4

-9 +/- sqrt 49/ 4

-9 +/- 7 /4 = -2/4 and -16/4         x = -1/2 x = -4

500

Solve the following quadratic equation by using the quadratic formula: 4x² - 17x - 15 = 0

x = -b +/- sqrt(b² - 4(4)(-15) /2a

x = 17 +/- sqrt(289 + 240) /8

x = 17 +/- sqrt (529) /8 = x = 17 +/- 23 /8

x = 40/8 x = -6/8  or

x = 5 x = -3/4

Solving Quadratics

100

Find x.  

x²+6x+9 = 0

What is 3.

200

Find x.  

x²- 4 = 0

What is 2 or -2.

300

Find x.  

3x²+x = 14

What is -7/3 and 2

400

If a number is added to twice its square, the result is 6.  Find the number.

What is -2. 

500

Find three consecutive positive integers such that the square of the first increased by the last, is 22.  

What is 4,5,6.