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Solving Quadratic Equations

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 = ax2 + 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 = ax2 + bx + c by graphing
The solutions to 0 = ax2 + bx + c are the x-intercepts of the graph of the
equation
y = ax2+ 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 10x2 - 5x –50 = 0 by graphing

Solution - Graph the quadratic function 10x2 - 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 10x2 - 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 ax2+ bx + c = 0

Unlike graphing where approximate solutions may be necessary, the quadratic
formula gives exact solutions to any equation ax2+ 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 2x2+ 5x = 25

Solution
Step 1 - Write the equation in the form ax2+ 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 = x2 - 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 )

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