9.6 THE QUADRATIC FORMULA:

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Presentation transcript:

9.6 THE QUADRATIC FORMULA: Quadratic Formula: Formula used to find the solution(s) of any quadratic equation. If ax2+bx+c = 0 and a ≠ 0, then

GOAL:

x2-8=2x QUADRATIC EQUATION: Ex: What are the solutions to? Use the quadratic formula. x2-8=2x

x2-8=2x  x2-2x-8 =0 x = -2, 4 SOLUTION:  a = 1 , b = -2 and c = -8 We must first put the equation in ax2+bx+c=0 form. x2-8=2x  x2-2x-8 =0  a = 1 , b = -2 and c = -8 x = -2, 4

YOU TRY IT: Ex: What are the solutions to? Use the quadratic formula. x2-4x=21

x2-4x=21  x2-4x-21 =0 x = -3, 7 SOLUTION: We must first put the equation in ax2+bx+c=0 form. x2-4x=21  x2-4x-21 =0  a = 1 , b = -4 and c = -21 x = -3, 7

REAL-WORLD: In the shot put, An athlete throws A heave metal ball Through the air. The arc of the ball is modeled by the equation: -0.04x2+.84x+2. Where x is the horizontal distance. How far from the athlete will the ball land?

x cannot be negative: x = 23.16 meters SOLUTION: The given equation is already in standard form: -0.04x2+0.84x+2 = 0  a = -0.04 , b = 0.84 and c = 2 x cannot be negative: x = 23.16 meters

VIDEOS: SOLVING BY FACTORING Solving by factoring: http://www.khanacademy.org/math/algebra/quadratics/factoring_quadratics/v/Example%201:%20Solving%20a%20quadratic%20equation%20by%20factoring

VIDEOS: SOLVING BY FACTORING Solving by factoring: http://www.khanacademy.org/math/algebra/quadratics/factoring_quadratics/v/Example%202:%20Solving%20a%20quadratic%20equation%20by%20factoring http://www.khanacademy.org/math/trigonometry/polynomial_and_rational/quad_formula_tutorial/v/solving-quadratic-equations-by-completing-the-square

CLASSWORK: Page 508-509: Problems: 4, 7, 15, 21, 25, 36, 37.