Name__________________________________
Period__________
1.Which is a quadratic function? Explain why:
A.y + 3x 2 = 5
A is a quadratic because it can be written in the form y = ax^2 + bx + c = 0
B.y = 3x + 5
B is not a quadratic, it is a straight line
2.Which function has a graph that opens downward? Explain why:
A.−x 2 + y = 0
A can be written y = ax^2 + bx + c = 0, which means that y = x^2. a=1 which is >0 so is
opens up
B.y = x 2 − 1
A can be written y = ax^2 + bx + c = 0, which means that y = x^2. a=1 which is >0 so is
opens up
3. What is the vertex of the parabola graphed below?
A. (−3, 0)
C. (1, 0)
B. (−4, −1)
D. (−1, −4)
D is the correct answer
4.What are the zeros of the function graphed below?
A. −1 and 0
B.−2 and 0
C. 0 and 1
D. 0 and 2
B is the answer
5.What is the vertex of the graph of y = −2x 2 + 8x − 3? Explain how you chose:
A. (2, 5)
C. (−2, 5)
B. (−2, −27)
D. (4, −11)
A is the answer, I used a graphing calculator and looked at the table
6.What function is shown on the graph below? Explain how you chose:
A. y = −x 2 − 4x
B. y = x 2 − 4x
C. y = −x 2 + 4x
D. y = x 2 + 4x
B is the answer, it opens upward so that left b and d, and I plugged in +2 and got -4
7.The height in feet of a rocket launched from the ground can be modeled by the function
f(x) = −16x 2 + 96x, where x is the time in seconds after it is launched.
What is the rocket’s maximum height? Explain how you chose:
A. 144 feet
C. 288 feet
B. 240 feet
D. 432 feet
A is the answer, I used the graphing calculator and the table. I also found the zeros at 0 and 6
and then plugged 3 into the function.
8.Which function’s graph has an axis of symmetry of x = 2?
A. y = −3x 2 − 12x + 6
B. y = 3x 2 − 6x + 12
C. y = 3x 2 + 12x + 6
D. y = −3x 2 + 12x + 6
D is the answer. Axis is = -b/2a = -12/2(-3) = 12/6 = 2
9. f(x) = x 2 and g(x) = 3x 2 + 1. Which statement is true?
A
B
C
D
g(x) is wider than f(x).
g(x) is narrower than f(x).
g(x) and f(x) have the same vertex.
g(x) and f(x) have different axes of symmetry.
B is the answer, the bigger a is the narrower the graph.
10. Which function has a vertex different from the vertex of the graph of f(x) = 2x 2 + 1?
A. g(x) = x 2 + 4
B. g(x) = 3x 2 + 1
C. g(x) = x 2 + 1
D. g(x) = −2x 2 + 1
A is the answer, the vertex is determined by C and a is different than the other 3.
11.The vertex of a quadratic function is in the second quadrant. The related equation has no
real solutions. Which statement is true?
A The graph opens down.
B The graph opens up.
C The y-intercept is 0.
D The axis of symmetry is x = 0.
B is the answer because there are no x intercepts
12. Use the graph to find the solutions of
x 2 − 2x − 3 = 0.
A. −1 and 3
B. −1 and −3
A is the answer
C. 1 and −3
D. 1 and 3