Review: Solving Quadratic Equations

Solve

Quadratic Facts

Features of Parabolas

Quadratic Formula

What is it?

100

Solve:

0=(x+3)(x-2)

x=-3, 2

100

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

x-intercepts

100

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

x-intercept

100

What is the quadratic formula?

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

100

Is this a quadratic equation? Explain.

x²+ 6x + 9 = 0

Yes because it is the quadratic form y = ax² + bx + c where a does not equal zero.

200

Solve the following quadratic equation.

x^2 + 3x + 2 = 0

x=-2,-1

200

What are the three different types of solutions we can have when solving quadratics

No solution, One solution or Two solutions

200

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

Vertex

200

Identify a, b and c in the following equation:

x² + 6x + 5 = 0

a = 1; b = 6; c = 5

200

Is this a quadratic equation? Explain your answer.

y = 9x³+ x²- x + 8

No because the first x is cubed.

300

Solve the following quadratic equation.

x^2 - 6x + 5 = 0

x = 5 ; x = 1

300

How do we know a quadratic function does not have solutions when looking at a graph?

It does not touch the x-axis

300

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

Axis of Symmetry

300

Identify a, b and c in the following equation:

x² - 9x + 20 = 9

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

300

Solve the following

x² - 5x - 24 = 0

x = 8, x = -3

400

Solve the following quadratic equation.

x^2 - 6x - 27 = 0

x = 9 ;x = -3

400

Why is the quadratic formula useful for solving quadratic equations?

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

400

The _________ ________ is a formula used to find the zeros of a quadratic function.

Quadratic formula

400

Solve the following quadratic equation by using the quadratic formula: 2x² + 9x + 4 = 0

x = -1/2 x = -4

400

Solve the following:

2x²+39 = -18x

x=9/2+-sqrt(3)/2

500

Solve the following quadratic equation.

2x² - 5x - 3 = 0

x = -1/2 ,3

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.

500

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

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

Answers will vary.

500

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

x = 5 x = -3/4

500

Solve

x² = 2x + 48

x = 8 x = -6