Quadratic equations

Graphing and Solving with x2

The typical form of a y = x2 graph:

Quadratic equationsQuick Exercise:

Graph the following on the same axes:

• y = x2

• y = x2 + 2

• y = x2 - 2x

The form of a y = x2 + bx + c graph:

General Form of Quadratics

The general form is either:

• y = ax2 + bx + c

Or

• ax2 + bx + c = 0

General Form of Quadratics

The general form is either:

• y = ax2 + bx + c used for graphing

Or

• ax2 + bx + c = 0

General Form of Quadratics

The general form is either:

• y = ax2 + bx + c used for graphing

Or

• ax2 + bx + c = 0 when solving for x

For now, we will stick to when a = 1

Quadratics

• The equation for such a modified parabola is called a quadratic.

• Quadratics will always have a variable raised to the second power, like x2.

• Factoring is one way to find solutions to quadratic equations.

0 = x2 - 6x - 16

0 = (x - 8)(x + 2)

x = {-2, 8}

D2. What are the solutions to the

quadratic x2 - 2x - 3 = 0?x2 - 2x - 3 = 0

(x - 3)(x + 1) = 0

Set each factor to 0

x - 3 = 0

x = 3

x + 1 = 0

x = -1

x = -1 or x = 3

A. 1 and 3

B. -1 and -3

C. -1 and 3

D. 1 and -3

E. 1 and 2

So what about the y = x2 - 2x - 3 graph?

So what about the y = x2 - 2x - 3 graph?

So what about the y = x2 - 2x - 3 graph?

The graphCrossesThe x axis

Here

So what about the y = x2 - 2x - 3 graph?

The graphCrossesThe x axis

Herex = -1

So what about the y = x2 - 2x - 3 graph?

The graphCrossesThe x axis

And hereHerex = -1

So what about the y = x2 - 2x - 3 graph?

The graphCrossesThe x axis

Herex = -1

And herex = 3

So what about the y = x2 - 2x - 3 graph?

The graphCrossesThe x axis

Herex = -1

And herex = 3

So again we see our solution, x = -1 or x = 3

So what about the y = ax2 + bx + c graph?

The graphCrossesThe x axis

Herex = ?

And herex = ?

This time we may need to use the quadratic formula