Name: ______________________
Class: _________________
Date: _________
Math 20-1. 6.4 and 6.5 Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Which equation represents the quadratic function y = –(x + 7)2 – 8 in standard form?
a.
b.
____
y = –x2 – 14x – 49
y = –x2 – 14x – 41
c.
d.
y = –x2 – 14x – 57
y = –(x2 – 14x + 41)
2. Which quadratic function defines this parabola in vertex form?
a.
b.
y = (x – 8)2 – 4
y = 2(x – 7)2 – 3
c.
d.
y = (x – 9)2 – 4
y = 0.5(x – 8)2 – 3
Short Answer
3. Sketch the graph of f(x) = 2(x – 1.5)2 + 3, then state the domain and range of the function.
.
4. Determine the value of a given that (–9, –8) satisfies the quadratic function
f(x) = a(x + 4)2 – 3.
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ID: A
Name: ______________________
ID: A
5. Determine the equation of a parabola with vertex (3, –3) and point (7, –19).
.
6. How many zeros does f(x) = –0.5(x – 3)2 – 18 have? Test your prediction by graphing the function on
your calculator.
.
Problem
7. Gordon and Hanna are standing 10 ft apart, playing badminton. They use a video camera to determine
that the path of the birdie on one volley is defined by the function
h(x) = –0.04(x – 5)2 + 7, where x is the horizontal distance, measured in feet, from Gordon toward
Hanna.
a) Determine the axis of symmetry of the parabola.
b) What was the highest point of the birdie's path?
c) How high was the birdie from the ground when it was 2.5 ft from Gordon?
d) What is the range for this function? Justify your answer.
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ID: A
Math 20-1. 6.4 and 6.5 Review
Answer Section
MULTIPLE CHOICE
1. C
2. A
SHORT ANSWER
3.
y ≥ 1.5, x ∈ R
4. a = –0.2
5. f(x) = –(x – 3)2 – 3
6. Vertex is at (3, –18) and a < 0 so graph opens downward.
No zeroes; the graph is below the x-axis.
PROBLEM
7. a) The vertex is (5, 7), so the axis of symmetry is x = 5.
b) The vertex is (5, 7), so the highest point of the birdie's path is 7 ft.
c) Substitute 2.5 for x in the equation and solve for h(2.5).
h(2.5) = –0.04(2.5 – 5)2 + 7
h(2.5) = –0.04(6.25) + 7
h(2.5) = 6.75
The birdie is 6.75 ft from the ground.
d) 0 ≤ x ≤ 10; Gordon and Hanna are standing 10 ft apart.
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