Warm-up

Evaluate each ex pression 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 de termine 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 )