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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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The Quadratic Formula The solutions of a quadratic equation in the form ax 2 + bx + c = 0, where a0, are given by the formula .

Note that this formula can be used to find the solutions to any quadratic equation.

Example 1

Solve x 2 + x - 2 = 0 by using the Quadratic Formula.

Solution

In this equation, a = 1, b = 1, and c = -2.

Note that the discriminant b 2 - 4ac = 9. Since this is greater than zero, we expect two solutions. Indeed, the Quadratic Formula says that there are two solutions.

Check these solutions by factoring and graphing.

x 2 + x - 2 = (x - 1)(x + 2)

x - 1 = 0 or x + 2 = 0

x = 1 or x = -2

Example 2

Solve -x 2 - 2x + 2 = 0 by using que Quadratic Formula.

Solution

In this equation the a = -1, b = -2 and c = 2.

So the solutions are and These numbers are approximately - 2.732 and 0.732. Notice that we could not have solved this equation by factoring, since the function y = -x 2 - 2x + 2 does not have integer roots.