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Do Now 4/3/19

Take out HW from last night. Text p. 465, #6-28 evens Copy HW in your planner. Text p. 447, #31, 35, 39, 43, 57 Text p. 455, #19, 23, 29, 49, 61 Text p. 465, #15, 17, 21, 23 Quiz sections 8.4-8.6 Thursday

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Do Now 4/3/19

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  1. Take out HW from last night. • Text p. 465, #6-28 evens • Copy HW in your planner. • Text p. 447, #31, 35, 39, 43, 57 • Text p. 455, #19, 23, 29, 49, 61 • Text p. 465, #15, 17, 21, 23 • Quiz sections 8.4-8.6 Thursday • Search your computer or re-download the “How Are You Doing?” Chapter 8 Graphing Quadratic Functions worksheet from Schoology. Do Now 4/3/19

  2. HomeworkText p. 465, #6-28 evens

  3. HomeworkText p. 465, #6-28 evens

  4. Learning Goal • SWBAT graph quadratic functions Learning Target • SWBAT review and practice graphing and writing quadratic functions in vertex form, intercept form and choosing functions to model data and write functions to model data

  5. Section 8.4 “Graphing f(x) = a(x – h)² + k” Vertex Form of a quadratic function is the form f(x) = a(x – h)2 + k, where a ≠ 0. The vertex of the graph of the function is (h, k) and the axis of symmetry is h.

  6. Find the axis of symmetry and vertex of the graph of the function f(x) = a(x – h)2 + k Vertex: (h, k) Axis of Symmetry: x = h y = -6(x + 4)2 - 3 y = -4(x + 3)2 + 1 Axis of Symmetry: Axis of Symmetry: x = -4 x = -3 Vertex: Vertex: (-4, -3) (-3, 1)

  7. Graph: y = a(x – h)² + k. Compare to f(x) = x2 y = 3(x – 2)² – 1 y = 3(x - 2)² - 1 “Parent Quadratic Function” y = x² Axis of x = h symmetry: x = 2 Vertex: (h, k) (2, -1) 1 2 0 11 x-axis The graph of y is a vertical stretch by a factor of 3, a horizontal translation right 2 units and a vertical translation down 1 unit. y-axis

  8. Write a quadratic function in vertex form whose graph has the given vertex and passes through the given point. Vertex; (1,2); passes through (3, 10) y = a(x - h)2 + k y = a(x - 1)2 + 2 10 = a(3 - 1)2 + 2 10 = a(2)2 + 2 10 = 4a+ 2 8 = 4a y = 2(x - 1)2 + 2 2 = a

  9. Section 8.5 “Using Intercept Form” Intercept Form of a quadratic function is the form f(x) = a(x – p)(x – q), where a ≠ 0. The x-intercepts are p and q and the axis of symmetry is .

  10. Find the axis of symmetry, vertex, and zeros of the function f(x) = a(x – p)(x – q) Axis of Symmetry: x = Intercepts: p, q y = -(x + 1)(x – 5) y = (x + 6)(x – 4) Zeros: x = -6 & 4 Zeros: x = -1 & 5 Axis of Symmetry: Axis of Symmetry: x = -1 x = 2 Vertex: Vertex: (2, 9) (-1,-25)

  11. Graph: y = a(x – p)(x – q). Describe the domain and range. y = -5x2 + 5x y = -5x2 + 5x Write in INTERCEPT form y = -5x(x - 1) Intercepts: x = 0; x = 1 Axis of x = symmetry: x = 1/2 Vertex: y = -5x(x + 1) x-axis y = -5(1/2)(1/2 + 1) (1/2, 5/4) The domain of the function is ALL REAL NUMBERS. The range of the function is y ≤ 5/4. y-axis

  12. Zeros of a Function an x-value for which f(x) = 0. A zero of a function is an x-intercept of the graph of the function. f(x) = -12x2 + 3 Graph (Standard Form) Intercept Form (Factor) To find the zeros of a function, graph the function and locate the x-intercepts. f(x) = -12x2 + 3 f(x) = -3(4x2 – 1) f(x) = -3(2x – 1)(2x + 1) x = ½ and -½

  13. Section 8.6 “Comparing Linear, Exponential, and Quadratic Functions” Quadratic Function Linear Function Exponential Function y = mx + b y = ax2+bx+c y = a(b)x

  14. Comparing Linear, Exponential, and Quadratic Functions Differences and Ratios Linear Function the first differences are constant y = mx + b Exponential Function consecutive y-values are common ratios y = a(b)x Quadratic Function the second differences are constant y = ax2+bx+c

  15. Tell whether the table represents a linear, exponential, or quadratic function. Then write the function. The second differences are constant. Therefore, the function is quadratic. y = a(x – p)(x – q) y = a(x - 4)(x - 8) 12 = a(2 - 4)(2 - 8) y = 1(x - 4)(x - 8) 12 = a(-2)(-6) y = x2 -12x + 32 12 = 12a 1 = a

  16. Tell whether the table represents a linear, exponential, or quadratic function. Then write the function. The first differences are constant. Therefore, the function is linear. Common difference (slope) Y-value when x = 0.

  17. Tell whether the table represents a linear, exponential, or quadratic function. Then write the function. Consecutive y-values have a common ratio. Therefore, the function is exponential. Y-value when x = 0. Commonratio.

  18. Scavenger Hunt

  19. Homework • Text p. 446, #31, 35, 39, 43, 57 • Text p. 455, #19, 23, 29, 49, 61 • Text p. 465, #15, 17, 21, 23 • Quiz sections 8.4-8.6 Thursday

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