Warm-up

Evaluate each expression if a = 6, b = -2, and c = 12.

Today we will:

1. Solve problems about situations modeled by parabolas . Last section in the

book!

Following class period we will:

1. Review key concepts

**10-8 Solving Quadratic Equations **

o Quadratic equation – an equation that can written in the form an equation

0 = ax^{2} + bx + c, where a, b, and c are numbers and a ≠ 0.

o Quadratic formula – the formula is used to find the solutions of a

quadratic equation.

Today we will solve the quadratic equations by…

• Graphing (the x- intercepts are the solutions )

• Using the quadratic formula

**Solving 0 = ax**^{2} + bx + c by graphing

The solutions to 0 = ax^{2} + bx + c are the x-intercepts of the graph of the

equation y = ax^{2}+ bx + c.

One way to solve is by drawing an accurate graph. If the graph doesn’t cross

the x-axis at points that correspond to integral units on the grid, the
solutions

will be approximations.

Example 1:

Solve 10x^{2} - 5x –50 = 0 by graphing

Solution - Graph the quadratic function 10x^{2} - 5x –50 = y

Step 1 – Make a table of values.

Step 2 – Use the table to draw a graph

Step 3 – Read the x-intercepts from the graph.

The x-intercepts are at –2 and 2.5,

so the solutions of 10x^{2} - 5x –50 = 0 are **x = -2 and x = 2.5.**

Check your solution. Substitute –2 and 2.5 into the
original equation.

**Using the quadratic formula to solve ax**^{2}+ bx + c = 0

Unlike graphing where approximate solutions may be necessary, the quadratic

formula gives exact solutions to any equation ax^{2}+ bx + c = 0.

Often the solutions involve square roots of numbers that are not perfect

squares. In such cases, you can approximate the solutions or give the exact

solutions in square root form .

Example 2:

Use the quadratic formula to solve 2x^{2}+ 5x = 25

Solution

Step 1 - Write the equation in the form ax^{2}+ bx + c = 0 and determine the

values of a , b, and c.

Step 2 – Use the quadratic formula.

Check your solutions – substitute 2.5 and –5 in the
original equation.

Example 3:

Use the quadratic formula to solve 0 = x^{2} - 11x + 18

Solution

Step 1 - Determine the values of a, b, and c.

Step 2 – Use the quadratic formula.

Check your solutions – substitute 9 and 2 in the original
equation.

Yep, both work!

In Summary …

To solve quadratic equations we can…

• Graph to find the x-intercepts

• Use the quadratic formula

• Factor ( and use the Zero - Product Property )