Which of the following could be the graph of f(x) = 1/3(x − 3)2 − 4?

A. graph is f(x) = ? (x - 3)^2 - 4 B. graph is y = ? (x + 3)^2 - 4
C. graph is y) = ? (x - 3)^2 - 4 D. graph is y = ? (x - 4)^2- 3

A
Correct! The parabola is wider than the parent graph and has been translated 3 units to the right and 4 units down.

B
Incorrect. Since h = 3 in the equation, the graph should have shifted 3 units to the right.

C
Incorrect. The graph of a quadratic function is a parabola.

D
Incorrect. Since h = 3 and k = - 4 in the equation, the graph should have shifted 3 units to the right and 4 units down.

Which of the tables shown below represent the ordered pairs that lie on the graph of y = 2x2 – x – 1?

A.
x
y
-2
-3
-1
-2
0
1
1
1
B.
x
y
-1
0
0
-1
1
0
2
1
C.
x
y
-4
19
-2
5
0
-1
2
1
D.
x
y
-6
77
-3
20
0
-1
3
14

A
Incorrect. Did you substitute and simplify correctly?

B
Incorrect. Did you substitute and simplify correctly?

C
Incorrect. Did you substitute and simplify correctly?

D
Correct! All of these points lie on the graph of y = 2x^– x – 1.

Which of the following statements best represents the quadratic function y = 2x2 + 8x − 10?

A. The vertex is at (-4, -10) and the axis of symmetry is x = -4.
Incorrect. Remember that the formula to find the x-coordinate of the vertex and the axis of symmetry is x = - b/2a.

B. The vertex is at (2, 14) and the axis of symmetry is x = 2.
Incorrect. Remember that the formula to find the x-coordinate of the vertex and the axis of symmetry is x = - b/2a.

C. The vertex is at (-2, -18) and the axis of symmetry is x = -2.
Correct! The parabola opens up and the lowest point is at (-2, -18). The vertical line that passes through this point is x = -2.

D. The vertex is at (-2, -18) and the axis of symmetry is y = -18.
Incorrect. The line y = -18 is horizontal. The axis of symmetry for a parabola must be vertical.

During a football game a punter kicked the ball. The path the football traveled during the kick can be modeled using the equation y = -.035x2 + 1.6x + 1, where x measures the distance in yards the football travels and y measures the height of the football in yards. What is the maximum height of the football during the punt?

A. 17 yards
Correct! Since the parabola opens down, the maximum height occurs at the y-coordinate of the vertex.

B. 20 yards
Incorrect. Remember that the maximum height is represented by the y-coordinate of the vertex.

C. 40 yards
Incorrect. Remember that the maximum height is represented by the y-coordinate of the vertex.

D. 41 yards
Incorrect. Remember that the maximum height is represented by the y-coordinate of the vertex.

During the 4th of July celebration, Sam lit a rocket and it shot into the air. The height of the rocket during its flight can be modeled by the equation f(t) = -16t2 + 80t where t represents the time in seconds after the rocket flew into the air and f(t) represents the height in feet of the rocket at time t. At what time was the rocket 64 feet above the ground?

A. After 1 second
Incorrect. Your answer is partially correct. At t = 1 second, the rocket is at a height of 64 feet on its way up.

B. After 2.5 seconds
Incorrect. The rocket reaches its maximum height of 100 feet at t = 2.5 seconds.

C. After 4 seconds
Incorrect. Your answer is partially correct. At t = 4 seconds, the rocket is at a height of 64 feet on its way down.

D. After 1 and 4 seconds
Correct! Since the rocket reaches a maximum height of 100 feet, it must be 64 feet above the ground twice, once on the way up and again on the way down.