# Solving Quadratic Equations Using Completing the Square and the Quadratic Formula.

## Presentation on theme: "Solving Quadratic Equations Using Completing the Square and the Quadratic Formula."— Presentation transcript:

Completing the Square Solve x² - 6x - 16 = 0. Can you solve this by factoring? Solve x² - 6x - 16 = 0. Can you solve this by factoring?

Completing the Square Another way to solve x² - 6x - 16 = 0 is by completing the square. x² - 6x - 16 = 0 Another way to solve x² - 6x - 16 = 0 is by completing the square. x² - 6x - 16 = 0

Example 1 x² + 8x - 20 = 0

Example 2 2a² - 11a - 21 = 0

Example 3 3n²+ 7n + 7 = 0

Quadratic Formula / The roots of a quadratic equation of the form ax²+ bx + c = 0 with a≠0 are given by the formula:

Quadratic Formula Another way to solve x² - 6x - 16 = 0 is by using the quadratic formula. x² - 6x - 16 = 0 Another way to solve x² - 6x - 16 = 0 is by using the quadratic formula. x² - 6x - 16 = 0

Finding the Discriminant of a Quadratic Equation / The discriminant tells the nature of the roots of a quadratic equation or the zeros of the related quadratic function / In order to find the discriminant you use the part of the quadratic formula that is under the radical. b²- 4ac / The discriminant tells the nature of the roots of a quadratic equation or the zeros of the related quadratic function / In order to find the discriminant you use the part of the quadratic formula that is under the radical. b²- 4ac

Finding the Discriminant of a Quadratic Equation / If b²- 4ac > 0, then you will have two distinct real roots/zeros. / If b²- 4ac = 0, then you will have exactly one real root/zero. (The one real root is actually a double root) / If b²- 4ac < 0, then you will have no real roots/zeros. (Two distinct imaginary roots/zeros) / If b²- 4ac > 0, then you will have two distinct real roots/zeros. / If b²- 4ac = 0, then you will have exactly one real root/zero. (The one real root is actually a double root) / If b²- 4ac < 0, then you will have no real roots/zeros. (Two distinct imaginary roots/zeros)

Find the discriminant of each equation and describe the nature of the roots of the equation. Then solve the equation by using the quardatic formula. 1.) m²+ 12m + 36 = 0 2.) t²- 6t + 13 = 0