Starman: 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 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 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

Will the graph of the following equation on up or down? -3x² + 2x + 4 = 0

Down because a is negative when in standard form. 

500

Name the x-intercepts of the parabola described by the following quadratic equation. y = 3(x - 11)(x + 7). 

x = 11 and x = -7

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 in half.

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.

The Discriminant

100

What expression is used to find the discriminant? 

b² - 4ac

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

Use the discriminant to determine if the following trinomial is prime or factorable. x² + 14x + 35

Not factorable because 56 is not a perfect square

500

How many real solutions does the equation below have? 2x² -3x + 2 = 0

Two real solutions because 1 is greater than zero

More Factoring

100

How many solutions to the following equation are there? Find them. x²+6x+9 = 0

One solution, x = -3 

200

Can you solve the following equation using factoring? Why or why not? 

-x²- 4 = 0

No. It is not factorable. 

300

Write the following equation in factored form. y = x² - 7x - 30 

y = (x - 10) (x + 3) 

400

Find the vertex of the following parabola from the equation y = (x + 1)(x - 3).

(1, -4)

500

Name the x-intercepts of the parabola described by the following quadratic equation. y = (0.4x + 2)(x - 9)

x = -5 and x = 9