5.8 c - 6 x-7 Discriminant of a Quadratic • The...

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1 Warm Up • 1) Write the equation in standard form: • 2) Evaluate the expression for a = 1 b = -6 c = -7 y = - 2 x ( x - 1) + ( x + 1) 2 b 2 - 4 ac Objectives • To use the Quadratic formula to find the zeros of an equation. • To understand the Discriminant of an equation. KEY TERMS The Quadratic Formula The Discriminant Methods for Finding Zeros • What are the ZEROs? – Algebraically – Geometrically • Methods: – Factoring, GCF’s, Graphing, Completing the Square WHAT IF NONE OF THESE WORK? USE THE QUADRATIC FORMULA Standard Form Coefficients • General Standard Form: • Example Equation: a = b = c = y = ax 2 + bx + c y = 3 x 2 - 5 x - 2 The Quadratic Formula x = - b ± b 2 - 4 ac 2 a ax 2 + bx + c = 0 Using the Quadratic Formula • Find the X value the makes Y=0 y = 3 x 2 - 5 x - 2 x = - b ± b 2 - 4 ac 2 a

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2 You Try! • Find the Zeros of the Equation: 2 x 2 = -
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Unformatted text preview: 6 x-7 Discriminant of a Quadratic • The Discriminant is: • The Discriminant is a quick tool to see how many solutions exist. x =-b ± b 2-4 ac 2 a b 2-4 ac Discriminant Information Value # Solutions Graph D > 0 Two Real ? D = 0 One Real ? D < 0 No Real ? Two Imaginary D = b 2-4 ac ⇒ ⇒ ⇒ Using The Discriminant • Determine the type AND the number of solutions: x 2 + 6 x + 8 = You Try! • Find the Discriminant of the following equations: 5 4 8 2---= x x y 1 6 9 2 +-= x x y Homework • P.289 1 - 5, 11, 14, 22, 23, 34 - 37, 57-59, 66 Extra Credit ( Use a separate sheet of paper ) p. 291 68c, 69, 70 SHOW YOUR WORK! SHOW YOUR WORK! SHOW YOUR WORK! SHOW YOUR WORK!...
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This note was uploaded on 05/13/2011 for the course MTH 98 taught by Professor Johnson during the Fall '09 term at Grand Valley State.

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5.8 c - 6 x-7 Discriminant of a Quadratic • The...

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