1. Do Now 4/1/19 Take out HW from last night. Copy HW in your planner.
Text p. 456, #46-52 evens, evens
Copy HW in your planner.
Puzzle Time worksheet 8.5
Quiz sections 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).

2. 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

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

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

5. 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

6. 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

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

8. 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)

9. 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

10. 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

11. Cubic Functions

12. 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)

13. 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

14. 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

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

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

17. Homework
Puzzle Time worksheet 8.5