Name: ________________________ Class: ___________________ Date: __________
ID: A
Algebra II Honors Test Review 5-1 to 5-3
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. Which is the graph of y = −2(x − 2) 2 − 4?
a.
b.
c.
d.
Short Answer
Determine whether the function is linear or quadratic. Identify the quadratic, linear, and constant terms.
2. y = (x + 1)(6x − 6) − 6x 2
3. f(x) = (3x + 2)(−6x − 3)
1
Name: ________________________
ID: A
Identify the vertex and the axis of symmetry of the parabola. Identify points corresponding to P and Q.
4.
5.
6. Find a quadratic function to model the values in the table. Predict the value of y for x = 6.
x
y
–1
2
0
–2
3
10
2
Name: ________________________
ID: A
7. A manufacturer determines that the number of drills it can sell is given by the formula D = −3p 2 + 180p − 285,
where p is the price of the drills in dollars.
a. At what price will the manufacturer sell the maximum number of drills?
b.
What is the maximum number of drills that can be sold?
8. Use vertex form to write the equation of the parabola.
9. Identify the vertex and the y-intercept of the graph of the function y = −3(x + 2) 2 + 5.
10. Write y = 2x 2 + 12x + 14 in vertex form.
Write the equation of the parabola in vertex form.
11. vertex (–4, 3), point (4, 131)
12. vertex (0, 3), point (–4, –45)
3
Name: ________________________
ID: A
13. Graph y = 2x 2 − 7.
14. Graph y = x 2 + 3x + 2. Identify the vertex and the axis of symmetry.
15. Graph y = (x − 7) 2 + 5.
4
Name: ________________________
ID: A
16. Use the graph of y = (x − 3) 2 + 5.
a.
If you translate the parabola to the right 2 units and down 7 units, what is the equation
of the new parabola in vertex form?
b.
If you translate the original parabola to the left 2 units and up 7 units, what is the
equation of the new parabola in vertex form?
c.
How could you translate the new parabola in part (a) to get the new parabola in part (b)?
5
ID: A
Algebra II Honors Test Review 5-1 to 5-3
Answer Section
MULTIPLE CHOICE
1. A
SHORT ANSWER
2. linear function
linear term: 0x
constant term: –6
3. quadratic function
quadratic term: −18x 2
linear term: −21x
constant term: –6
4. (–1, –2), x = –1
P'(0, –1), Q'(–3, 2)
5. (–3, 1), x = –3;
P'(–2, 0), Q'(–5, –3)
6.
7.
8.
9.
y = 2x 2 − 2x − 2; 58
$30; 2,415 drills
y = 3(x + 2) 2 + 2
vertex: (–2, 5);
y-intercept: –7
10. y = 2(x + 3) 2 − 4
11. y = 2(x + 4) 2 + 3
12. y = −3x 2 + 3
13.
1
ID: A
14.
ÁÊÁ 3
1 ˜ˆ˜
3
vertex: ÁÁÁÁ − , − ˜˜˜˜ , axis of symmetry: x = −
ÁË 2
4 ˜¯
2
15.
16.
a.
b.
c.
y = (x − 5) 2 − 2
y = (x − 1) 2 + 12
left 4 units, up 14 units
2