Solving Quadratic Equations

Solve

100

Solve  (x - 7)(x + 2)

x² - 5x -14

200

Solve the following quadratic equation.

 x²+3x+2 = 0

x = -2 x = -1

300

Solve the following quadratic equation.

 x² - 6x + 5 = 0

x = 5 x = 1

400

Solve the following quadratic equation.

 x² - 6x - 27 = 0

x = 9 x = -3

500

Solve the following quadratic equation. 

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

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

Factored

500

When solving quadratic equations, what is another name for x-intercepts?

Solutions, Roots, Zeros of a function

Quadratic Equations

100

Identify a, b and c in the following equation: 

3x² + 4x + 1 = 0

a = 3; b = 4; c = 1

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 finding the solutions: 2x² + 9x + 4 = 0

x = -1/2 x = -4

500

Solve the following quadratic equation by finding the roots: 4x² - 17x - 15 = 0

x = 5 x = -3/4

What is it?

100

Is this a quadratic equation?

x² + 6x + 9 = 0

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

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

x² - 5x - 24 = 0

x = 8, x = -3

400

Solve the following: 

2x² +39 = -18x

x = -3.63397 

x = -5.36603

500

Solve 

x² = 2x + 48

x = 8   x = -6