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Section 5.8

Section 5.8. Modeling with Quadratic Functions. Remember the forms:. Standard: y = ax 2 + bx + c Vertex: y = a(x-h) 2 + k Intercept: y= a(x-p)(x-q). Write a quadratic function in vertex form for a parabola with zeros of 1 and 5 and vertex (3, -2). Y = a(x – h) 2 + k y = a(x-3) 2 - 2

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Section 5.8

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  1. Section 5.8 Modeling with Quadratic Functions

  2. Remember the forms: • Standard: y = ax2 + bx + c • Vertex: y = a(x-h)2 + k • Intercept: y= a(x-p)(x-q)

  3. Write a quadratic function in vertex form for a parabola with zeros of 1 and 5 and vertex (3, -2) • Y = a(x – h)2 + k • y = a(x-3)2 - 2 • Use one of the zeros to find a. (5,0) • 0 = a(5-3)2 – 2 • 0 = a(4) – 2 • 2 = 4a • a = ½ y = ½ (x – 3)2 - 2

  4. Write a quadratic function in vertex form for a parabola with vertex (4,1) passing through (2, -1) • Y = a(x – h)2 + k • y = a(x-4)2 + 1 • Use the point to find a. (2,-1) • -1 = a(2-4)2 + 1 • -1 = a(4) + 1 • -2 = 4a • a = - ½ y = -½ (x – 4)2 + 1

  5. Using the Graphing Calculator to find a quadratic model : • Put x into List 1 • Put y into List 2 • Stat, Calc, #5, enter • Y = ax2 + bx + c • a = #, b = #, c = # • Write the equation.

  6. Find a quadratic model for the data. y = -.026x2 + 1.59x + 4.3

  7. Find a quadratic model for the data. y = .55x2 – 3.25x + 12.82

  8. Assignment Section 5.8: page 309 # 7 – 9, 12 – 27 (÷3), 36 – 38 (on calc)

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