2017­3­15 graph factored form.notebook
Today Is Friday
3-17-17
Do Now:
-Take calculator
-Take out HW
-Copy down HW
-Text Section 8.5
page 455# 3-19 odd
HW Answers
March 17, 2017
2017­3­15 graph factored form.notebook
Today's Objective:
Graphing Quadratics in
Factored Form
March 17, 2017
2017­3­15 graph factored form.notebook
March 17, 2017
1) Water fountains are usually designed to give a specifi c visual effect. For example, the water fountain shown consists of streams of water that are shaped like parabolas. Notice how the streams are designed to land on the underwater spotlights. Write and graph a quadratic function that models the path of a stream of water with a maximum height of 5 feet, represented by a vertex of (3, 5), landing on a spotlight 6 feet from the water jet, represented by (6, 0).
2017­3­15 graph factored form.notebook
2) Graph f(x) = −(x + 1)(x − 5). Describe the domain and range.
3) Graph f(x) = 2x2 − 8. Describe the domain and range.
March 17, 2017
2017­3­15 graph factored form.notebook
March 17, 2017
Graph the quadratic function. Label the vertex, axis of symmetry, and x­intercepts. Describe the domain and range of the function.
4. f(x) = (x + 2)(x − 3) Graph the quadratic function. Label the vertex, axis of symmetry, and x­intercepts. Describe the domain and range of the function.
5. g(x) = −2(x − 4)(x + 1) 2017­3­15 graph factored form.notebook
March 17, 2017
The zeros of a quadratic function are the values of x when f(x)=0.
They are the x-intercepts of the function.
6) Find the zeros of f(x) = (x − 1)(x + 2).
Find the zeros of each function.
7. f(x) = −2x2 − 10x − 12 8. h(x) = (x − 1)(x2 − 16)
Find the zero(s) of the function.
9. f(x) = (x − 6)(x − 1) 11. h(x) = x(x2 − 1)
10. g(x) = 3x2 − 12x + 12 2017­3­15 graph factored form.notebook
March 17, 2017
12) Use zeros to graph h(x) = x2 − 2x − 3.
Write a quadratic function in standard form whose graph satisfies the
given condition(s).
13). vertex: (−3, 4)
2017­3­15 graph factored form.notebook
March 17, 2017
Write a quadratic function in standard form whose graph satisfies the
given condition(s).
14. passes through (−9, 0), (−2, 0), and (−4, 20)
Use zeros to graph the function.
15. f(x) = (x − 1)(x − 4) 16. g(x) = x2 + x − 12
12. passes through (−5, 0), (4, 0), and (3, −16)
2017­3­15 graph factored form.notebook
March 17, 2017
Write a quadratic function in standard form whose graph satisfies the given condition(s).
17. x­intercepts: −1 and 1 18. vertex: (8, 8)
Write a quadratic function in standard form whose graph satisfies the given condition(s).
19. passes through (0, 0), (10, 0), and (4, 12)
2017­3­15 graph factored form.notebook
20) Use zeros to graph f(x) = x3 − 4x.
21) The graph represents a cubic function. Write the function.
March 17, 2017
2017­3­15 graph factored form.notebook
Use zeros to graph the function.
22. g(x) = (x − 1)(x − 3)(x + 3)
March 17, 2017
2017­3­15 graph factored form.notebook
March 17, 2017
Use zeros to graph the function.
23. h(x) = x3 − 6x2 + 5x
24. The zeros of a cubic function are −3, −1, and 1. The graph of the function passes through the point (0, −3). Write the function.
2017­3­15 graph factored form.notebook
25) Use zeros to sketch the graphs of f(x) = −(x + 2)(x − 3) and
g(x) = x2 + 7x + 10.
March 17, 2017