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Published byKathleen Fox Modified over 4 years ago

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Objectives: To solve quadratic equations using the Quadratic Formula. To determine the number of solutions by using the discriminant.

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By Completing the Square of the following you will derive the Quadratic Formula. ax² + bx + c = 0

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Solve by using the quadratic equation: A. Write in standard form: (Set = to zero, like when factoring ) B. Divide by the common multiple, if there is one C. Identify a, b, and c. Then evaluate by using the quadratic formula.

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I. Solve by using the Quadratic Formula A.B.

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C.D.

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II. Discriminant Solutions to a quadratic are its x-intercepts. How many x-intercepts does a parabola have? Two interceptsOne interceptNone

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So, a parabola can have zero, one, or two x- intercepts. How can we know the numbers of x-intercepts without graphing?

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A. The Discriminant: b 2 - 4ac If b 2 - 4ac > 0, then there are two x- intercepts(two real solutions) If b 2 - 4ac = 0, then there is one x- intercept(one solution—double root) If b 2 - 4ac < 0, then there are NO x- intercepts(no real solutions - two conjugate imaginary roots)

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B. Evaluate the discriminant and describe the number and type of roots. 1. y = x 2 + 2x – 3 2.y = x 2 + 4x + 4 3.y = x 2 + x + 5

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Homework Pre-AP p. 11-23odd, 24, 25-37 odd, 38, 57- 63 odd

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