5.3 – Solving Quadratic Equations by Factoring. Ex. 1 Solve y = x 2 + 5x + 6 by factoring.

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Presentation transcript:

5.3 – Solving Quadratic Equations by Factoring

Ex. 1 Solve y = x 2 + 5x + 6 by factoring.

x 2 + 5x + 6 = y

Ex. 1 Solve y = x 2 + 5x + 6 by factoring. x 2 + 5x + 6 = y x 2 + 5x + 6 = 0

Ex. 1 Solve y = x 2 + 5x + 6 by factoring. x 2 + 5x + 6 = y x 2 + 5x + 6 = 0 (x )(x ) = 0

Ex. 1 Solve y = x 2 + 5x + 6 by factoring. x 2 + 5x + 6 = y x 2 + 5x + 6 = 0 (x )(x ) = 0 (x + 2)(x + 3) = 0

Ex. 1 Solve y = x 2 + 5x + 6 by factoring. x 2 + 5x + 6 = y x 2 + 5x + 6 = 0 (x )(x ) = 0 (x + 2)(x + 3) = 0

Ex. 1 Solve y = x 2 + 5x + 6 by factoring. x 2 + 5x + 6 = y x 2 + 5x + 6 = 0 (x )(x ) = 0 (x + 2)(x + 3) = 0 x + 2 = 0

Ex. 1 Solve y = x 2 + 5x + 6 by factoring. x 2 + 5x + 6 = y x 2 + 5x + 6 = 0 (x )(x ) = 0 (x + 2)(x + 3) = 0 x + 2 = 0

Ex. 1 Solve y = x 2 + 5x + 6 by factoring. x 2 + 5x + 6 = y x 2 + 5x + 6 = 0 (x )(x ) = 0 (x + 2)(x + 3) = 0 x + 2 = 0ORx + 3 = 0

Ex. 1 Solve y = x 2 + 5x + 6 by factoring. x 2 + 5x + 6 = y x 2 + 5x + 6 = 0 (x )(x ) = 0 (x + 2)(x + 3) = 0 x + 2 = 0ORx + 3 =

Ex. 1 Solve y = x 2 + 5x + 6 by factoring. x 2 + 5x + 6 = y x 2 + 5x + 6 = 0 (x )(x ) = 0 (x + 2)(x + 3) = 0 x + 2 = 0ORx + 3 = x = -2

Ex. 1 Solve y = x 2 + 5x + 6 by factoring. x 2 + 5x + 6 = y x 2 + 5x + 6 = 0 (x )(x ) = 0 (x + 2)(x + 3) = 0 x + 2 = 0ORx + 3 = x = -2

Ex. 1 Solve y = x 2 + 5x + 6 by factoring. x 2 + 5x + 6 = y x 2 + 5x + 6 = 0 (x )(x ) = 0 (x + 2)(x + 3) = 0 x + 2 = 0ORx + 3 = x = -2 OR x = -3

Ex. 2 Solve x 2 = 6x by factoring.

x 2 = 6x

Ex. 2 Solve x 2 = 6x by factoring. x 2 = 6x -6x

Ex. 2 Solve x 2 = 6x by factoring. x 2 = 6x -6x x 2 – 6x = 0

Ex. 2 Solve x 2 = 6x by factoring. x 2 = 6x -6x x 2 – 6x = 0

Ex. 2 Solve x 2 = 6x by factoring. x 2 = 6x -6x x 2 – 6x = 0 x(x – 6) = 0

Ex. 2 Solve x 2 = 6x by factoring. x 2 = 6x -6x x 2 – 6x = 0 x(x – 6) = 0 x = 0

Ex. 2 Solve x 2 = 6x by factoring. x 2 = 6x -6x x 2 – 6x = 0 x(x – 6) = 0 x = 0

Ex. 2 Solve x 2 = 6x by factoring. x 2 = 6x -6x x 2 – 6x = 0 x(x – 6) = 0 x = 0ORx – 6 = 0

Ex. 2 Solve x 2 = 6x by factoring. x 2 = 6x -6x x 2 – 6x = 0 x(x – 6) = 0 x = 0ORx – 6 = 0 x = 0

Ex. 2 Solve x 2 = 6x by factoring. x 2 = 6x -6x x 2 – 6x = 0 x(x – 6) = 0 x = 0ORx – 6 = x = 0

Ex. 2 Solve x 2 = 6x by factoring. x 2 = 6x -6x x 2 – 6x = 0 x(x – 6) = 0 x = 0ORx – 6 = x = 0OR x = 6

Ex. 3 Write a quadratic equation with roots 4 and -5. Write the equation in the form ax 2 + bx + c = 0, where a, b, and c are integers.

Ex. 3 Write a quadratic equation with roots 4 and -5. Write the equation in the form ax 2 + bx + c = 0, where a, b, and c are integers. x = 4x = -5

Ex. 3 Write a quadratic equation with roots 4 and -5. Write the equation in the form ax 2 + bx + c = 0, where a, b, and c are integers. x = 4x =

Ex. 3 Write a quadratic equation with roots 4 and -5. Write the equation in the form ax 2 + bx + c = 0, where a, b, and c are integers. x = 4x = x – 4 = 0 x + 5 = 0

Ex. 3 Write a quadratic equation with roots 4 and -5. Write the equation in the form ax 2 + bx + c = 0, where a, b, and c are integers. x = 4x = x – 4 = 0 x + 5 = 0 (x – 4)(x + 5) = 0

Ex. 3 Write a quadratic equation with roots 4 and -5. Write the equation in the form ax 2 + bx + c = 0, where a, b, and c are integers. x = 4x = x – 4 = 0 x + 5 = 0 (x – 4)(x + 5) = 0 x 2 + 5x – 4x – 20 = 0

Ex. 3 Write a quadratic equation with roots 4 and -5. Write the equation in the form ax 2 + bx + c = 0, where a, b, and c are integers. x = 4x = x – 4 = 0 x + 5 = 0 (x – 4)(x + 5) = 0 x 2 + 5x – 4x – 20 = 0 x 2 + x – 20 = 0