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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
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GOAL:
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x2-8=2x QUADRATIC EQUATION:
Ex: What are the solutions to? Use the quadratic formula. x2-8=2x
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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
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YOU TRY IT: Ex: What are the solutions to? Use the quadratic formula. x2-4x=21
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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
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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?
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x cannot be negative: x = 23.16 meters
SOLUTION: The given equation is already in standard form: -0.04x2+0.84x+2 = 0 a = , b = and c = 2 x cannot be negative: x = meters
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VIDEOS: SOLVING BY FACTORING Solving by factoring:
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VIDEOS: SOLVING BY FACTORING Solving by factoring:
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CLASSWORK: Page : Problems: 4, 7, 15, 21, , 36, 37.
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