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9.8 Using the Discriminant

9.8 Using the Discriminant. Objective: SWBAT use the quadratic formula to determine if the graph of a quadratic function will intersect the x-axis in zero, one, or two points. Mini Quiz 29. 1. Solve 2 x 2 – 3 x – 2 = 0 2. Graph y = - x 2 – 2 x + 1. Quick Review.

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9.8 Using the Discriminant

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  1. 9.8 Using the Discriminant Objective: SWBAT use the quadratic formula to determine if the graph of a quadratic function will intersect the x-axis in zero, one, or two points.

  2. Mini Quiz 29 1. Solve 2x2 – 3x – 2 = 0 2. Graph y = -x2 – 2x + 1

  3. Quick Review 1. What is the Vertex and Axis of Symmetryformula? 2. What is the Quadratic Formula?

  4. Overview Methods in Solving Quadratic Equations: Graphing Square Roots Factoring ( )( ) = 0 Completing the Square ( )2 Quadratic Formula Discriminant b2 - 4ac

  5. Discrimin… Discriminate – to note or observe a difference (according to www.dictionary.com ) Discriminant - a relatively simple expression that determines ... the nature of the roots, of a given equation or function (according to www.dictionary.com) Tells you the different number of times the graph crosses the x-axis (according to Ms. Ly in “plain Math English”) ???

  6. How many solutions?

  7. The Amazing Discriminant! How can you tell the numbers of solutions (roots, x-intercepts) without graphing the quadratic function? Use the Discriminant!!!

  8. How does it work? (negative)…no solution (zero)…1 solution (positive)…2 solutions

  9. Practicing with the Discriminant Find the number of solution(s) the quadratic function/equation has. 1. 0 = x2 + x + 1 2. y = x2 + 2x – 2 3. y = 2x2 + 4x + 4. -3x2 + 5x – 1 = 0 5. 23x2 – 2x = -5 Discriminant: b2 – 4ac Zero Two One Two Zero

  10. Wrap Up Discriminant • Discriminant b2 - 4ac • Tell you the number of solutions • –  0 • 0  1 • +  2 HW: P. 472 #1-9 all, 55-67 odd DLUQ: What does the discriminant tell you?

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