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# 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:

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

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.

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.

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.

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

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? ______________________________

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

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

Graphic Calculator Y-intercept 5 when x = 0

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