12.5 Completing the Square Goal: Solve a quadratic equation by completing the square.

Presentación del tema: "12.5 Completing the Square Goal: Solve a quadratic equation by completing the square."— Transcripción de la presentación:

1 12.5 Completing the Square Goal: Solve a quadratic equation by completing the square.

2 Standard 14.0 Students solve a quadratic equation by factoring or completing the square. Los estudiantes solucionan una equación cuadrática descomponiendola en factores o completando el cuadrado.

3 Standard 19.0 Students know the quadratic formula and are familiar with its proof by completing the square. Los estudiantes saben la fórmula cuadrática y son familiares con su prueba completando el cuadrado.

4 Standard 23.0 Students apply quadratic equations to physical problems, such as the motion of an object under the force of gravity. Los estudiantes aplican equaciones cuadráticas a los problemas de física, tales como el movimiento de un objeto bajo fuerza de la gravedad.

5 Vocabulary To complete the square of the expressions x 2 + bx, add the square of half the coefficient of x.

6 Example 1 Solve x 2 - 18x + 5 = 0 Leading coefficient a = 1, parabola opens ______ Linear coefficient b = -18 Y-intercept c = 5, x = ______ What kind of polynomial is it? ______________________________

7 Math Process Write original equation x 2 - 18x + 5 = 0 Subtract 5 from each side - 5 - 5 Simplify x 2 - 18x = - 5 Add the square of half of the linear coefficient to each side

8 Math Process Take square root from the first term and third term on the quadratic trinomial Factor the trinomial or write the left side as perfect square (x - 9) 2 = 76 Square root both sides

9 Graphic Calculator Y-intercept 5 when x = 0