Do Now 4/1/19 Take out HW from last night. Copy HW in your planner. Text p. 456, #46-52 evens, 58-74 evens Copy HW in your planner. Puzzle Time worksheet 8.5 Quiz sections 8.4-8.6 Thursday In your notebook, write a cubic function in Intercept form and Standard form with the following points. (-3, 0), (-1, 0), (1, 0) and (0, -3).

y = a(x – p)(x – q)(x – r) -3 = a(0 + 3)(0 + 1)(0 – 1) On Your Own Write a cubic function that passes through the points (-3, 0), (-1, 0), (1, 0) and (0, -3). y = a(x – p)(x – q)(x – r) -3 = a(0 + 3)(0 + 1)(0 – 1) -3 = a(3)(1)(-1) -3 = -3a Intercept form 1 = a y = (x+3)(x + 1)(x – 1) Standard form y = (x + 3)(x2 – 1) y = x3 + 3x2 – x - 3

Homework Text p. 456, #46-52 evens, 58-74 evens

Homework Text p. 456, #46-52 evens, 58-74 evens

Learning Goal Learning Target SWBAT graph quadratic functions SWBAT graph quadratic functions of the form f(x) = a(x – p)(x – q) and use characteristics to graph and write cubic functions

Section 8.5 “Using 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 .

The Graph of f(x) = a(x – p)(x – q) When a > 0, the graph opens UP. When a < 0, the graph opens DOWN.

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

y = -(x + 1)(x – 5) x-axis y-axis Graph: y = a(x – p)(x – q). Describe the domain and range. y = -(x + 1)(x – 5) y = -(x + 1)(x – 5) Intercepts: x = -1; x = 5 Axis of x = symmetry: x = 2 Vertex: y = -(x + 1)(x – 5) y = -(2 + 1)(2 – 5) (2, 9) x-axis The domain of the function is ALL REAL NUMBERS. The range of the function is y ≤ 9. y-axis

y = -5x2 + 5x y = -5x(x - 1) x-axis y-axis 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

Cubic Functions

Find the axis of symmetry, vertex, and zeros of the function f(x) = a(x – p)(x – q)(x – r) Intercepts: p, q, r Axis of Symmetry: x = & y = -(x + 1)(x – 5)(x – 9) y = 2x3 - 32x y = 2x(x + 4)(x – 4) Zeros: x = -1, 5, 9 Zeros: x = -4, 0, 4 Axis of Symmetry: Axis of Symmetry: x = -2, 2 x = 2 & 7 Vertex: (2, -63) (7, 32) Vertex: (-2, 48) (2,-48)

y = 2x3 - 8x y = 2x(x2 - 4) y = 2x(x - 2)(x + 2) x-axis y-axis x = -2; Graph: y = a(x – p)(x – q)(x – r). y = 2x3 - 8x y = 2x3 - 8x Write in INTERCEPT form y = 2x(x2 - 4) y = 2x(x - 2)(x + 2) Intercepts: x = -2; x = 0; x = 2 Axis of x = symmetry: x = -1 x = 1 Vertex: y = 2x3 – 8x y = 2x3 – 8x x-axis y = 2(-1)3 – 8(-1) y = 2(1)3 – 8(1) (-1, 6 ) (1, -6 ) y-axis

y = a(x – p)(x – q)(x – r) y = a(x - 0)(x - 2)(x – 5) Write a cubic function from the graph. Passes through the points (0, 0), (2, 0), (3, 12), (5,0) y = a(x – p)(x – q)(x – r) y = a(x - 0)(x - 2)(x – 5) 12 = a(3 - 0)(3 – 2)(3 – 5) 12 = a(3)(1)(-2) Intercept form 12 = -6a y = -2x(x - 2)(x – 5) -2 = a Standard form y = -2x(x2 – 7x + 10) y = -2x3 + 14x2 -20x

Graph the cubic function. On Your Own Graph the cubic function. f(x) = -x3 + 4x2 – 3x

Clock Partners With your 9:00 partner, complete Puzzle Time worksheet 8.5 on Schoology

Homework Puzzle Time worksheet 8.5