EXAMPLE 1 Solve a quadratic equation having two solutions Solve x 2 – 2x = 3 by graphing. STEP 1 Write the equation in standard form. Write original equation.

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EXAMPLE 1 Solve a quadratic equation having two solutions Solve x 2 – 2x = 3 by graphing. STEP 1 Write the equation in standard form. Write original equation. x 2 – 2x = 3 Subtract 3 from each side. x 2 – 2x – 3 = 0 STEP 2 Graph the function y = x 2 – 2x – 3. The x- intercepts are – 1 and 3. SOLUTION

EXAMPLE 1 ANSWER The solutions of the equation x 2 – 2x = 3 are – 1 and 3. Solve a quadratic equation having two solutions You can check – 1 and 3 in the original equation. x 2 – 2x = 3 (–1) 2 –2(–1) 3 = ? (3) 2 –2(3) 3 = ? 3 = 3 Write original equation. Substitute for x. Simplify. Each solution checks. CHECK

EXAMPLE 2 Solve a quadratic equation having one solution Solve – x 2 + 2x = 1 by graphing. SOLUTION STEP 1 Write the equation in standard form. Write original equation. – x 2 + 2x = 1 Subtract 1 from each side. – x 2 + 2x – 1 = 0

EXAMPLE 2 Solve a quadratic equation having one solution STEP 2 Graph the function y = – x 2 + 2x – 1. The x- intercept is 1. ANSWERThe solution of the equation – x 2 + 2x = 1 is 1.

EXAMPLE 3 Solve a quadratic equation having no solution Solve x = 4x by graphing. SOLUTION STEP 1 Write the equation in standard form. Write original equation. x = 4x Subtract 4x from each side. x 2 – 4x + 7 = 0

EXAMPLE 3 Solve a quadratic equation having no solution STEP 2 Graph the function y = x 2 – 4x + 7. The graph has no x -intercepts. ANSWER The equation x = 4x has no solution.

GUIDED PRACTICE for Examples 1, 2 and 3 Solve the equation by graphing. 1. x 2 – 6x + 8 = 0 ANSWER 2, 4 2. x 2 + x = – 1 ANSWER no solution 3. – x 2 + 6x = 9 ANSWER 3