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

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 solutions 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 in half.

Axis of Symmetry

400

Find the vertex and axis of symmetry of this parabola defined by y=4x²+16x-27

Vertex: (-2,-43)

Axis of Symmetry: x=-2

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(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

Completing the square

100

Which constant will complete the square

x²+24x+c

c=144

200

Find the constant that will complete the square, then factor. 

x²-20x+c

c=100

(x-10)²

300

Solve by completing the square

x²-12x+20=0

x=2, 10

400

Solve by Completing the square. Write square roots in simplest form.

x²+8x+13=0

x=-4+-sqrt(3)

500

Solve by Completing the Square. Write square roots in simplest form.

x²+18x=-57

x=-9+-2sqrt6