Name: ________________________ Class: ___________________ Date: __________
Quadratics Review
Multiple Choice
____
2
1. How is y = (x − 3) different from y = x2?
a.
c.
f(x) translated to the right 3 unit(s)
f(x) translated up 3 unit(s)
d.
b.
f(x) translated to the left 3 unit(s)
f(x) translated down 3 unit(s)
____
____
2. What is the y-intercept of y = 3x2 + 4x + 1?
a. 3
b. 4
2
1
3. Identify the vertex and axis of symmetry for y = 2x 2 + 4x − 10.
a.
b.
____
c.
d.
vertex: ( –1, – 6)
axis of symmetry: x = −1
vertex: ( –1, – 6)
axis of symmetry: x = − 6
c.
d.
vertex: ( 1, – 6)
axis of symmetry: x = − 6
vertex: ( –1, 6)
axis of symmetry: y = −1
4. Solve x 2 − 8x + 16 = 16 by completing the square.
a. –8, 8
c. 0, 8
b. –8, 0
d. 0, 0
1
ID: A
Name: ________________________
____
5. How is y = (x + 3) 2 + 4 different from y = x2?
a.
ID: A
c.
f(x) translated down 4 unit(s) and
translated to the left 3 unit(s)
f(x) translated down 4 unit(s) and
translated to the right 3 unit(s)
d.
b.
f(x) translated up 4 unit(s) and translated
to the left 3 unit(s).
f(x) translated up 4 unit(s) and translated
to the right 3 unit(s)
____
2
6. Identify the vertex and the axis of symmetry of the graph of the function y = 2(x + 2) − 4.
a. vertex: (–2, 4);
axis of symmetry: x = −2
b. vertex: (2, –4);
axis of symmetry: x = 2
c. vertex: (–2, –4);
axis of symmetry: x = −2
d. vertex: (2, 4);
axis of symmetry: x = 2
____
7. Write y = x 2 − 2x + 8 in vertex form.
a.
b.
y = (x + 1) 2 + 7
y = (x + 1) 2 − 7
c.
d.
2
y = (x − 1) 2 + 7
y = (x − 1) 2 − 7
Name: ________________________
____
8. Solve x 2 + 11x = −28 by factoring.
a. –4, –7
b. –4, 7
ID: A
c.
d.
4, 7
4, –7
9. Solve x 2 − 12x + 32 = 0 by factoring.
a. –4, 8
c. 4, 8
b. 4, –8
d. –4, –8
____ 10. What is the maximum or minimum value of y = -x2 + 8x + 3?
a. maximum; y = 19
c. minimum; y = 19
b. minimum; y = 4
d. maximum; y = 4
____ 11. Write a quadratic equations with the roots -1/3 and 4.
a. 3x2 - 11x - 4 = 0
c. x2 + 12x - 4 = 0
2
b. 3x - x - 4 = 0
d. 3x2 - 9x - 12 = 0
____
____ 12. Solve x 2 − 4x − 5 = 0 by graphing.
a.
c.
1, –5
b.
–1, 5
d.
1, –5
–1, 5
____ 13. Describe the types of solutions for x2 + 3x + 4 = 0. (Hint: Find the value of the discriminant.)
a. one rational root
c. two complex roots
b. two irrational roots
d. two rational roots
____ 14. The product of two consecutive numbers is 210. What are these two numbers?
a. 11, 12
c. 10, 11
b. 2, 105
d. 5, 42
3
Name: ________________________
ID: A
____ 15. Use the Quadratic Formula to solve 2x 2 + x − 4 = 0
a.
1
− ±
2
33
4
c.
1
− ±
4
33
4
b.
−4 ±
66
4
d.
1
− ±
2
33
2
____ 16. Use the Quadratic Formula to solve −x 2 + 6x − 5 = 0
a. −5, −1
c. −5, 11
b. 1, 5
d. 2, 10
____ 17. Solve x2 + 14x + 49 = 64 by completing the square.
a. 7, 8
c. 1
b. 1, -15
d. -1, 15
2
____ 18. Solve x + 6x + 13 = 0 by completing the square.
a. -3 + 2i, - 3 - 2i
c. -1, -5
b. -3 + 4i, -3 - 4i
d. 3 + 2i, 3 - 2i
____ 19. Solve x 2 + 8x + 15 = 0 by graphing.
a.
c.
–5, –3
5, 3
b.
d.
5, 3
–5, –3
4
ID: A
Quadratics Review
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
C
D
A
C
B
C
C
A
C
A
A
C
C
C
C
B
B
A
C
1