Which equation BEST represents the data from the table below?

1. -x² + 2x + 3
2. -x² − 3x - 2
3. x² + 2x + 1
4. x² − 3x − 4

A
Incorrect. This one has zeros at -1 and 3.

B
Correct! Zeros at -2 and -1.

C
Incorrect. This parabola will open upward.

D
Incorrect. This parabola opens upward and has zeros at -1 and 4.

Choose the BEST verbal description of the parabola represented by this table of values.

A. The function has two real, rational zeros and a minimum.
Incorrect. The graph has a maximum, not a minimum.

B. The function has two real zeros and a minimum.
Incorrect. The graph has a maximum, not a minimum.

C. The function has two real, rational zeros and a maximum.
Correct! The graph has a maximum, and the zeroes are -4 and 2 which are real rational numbers.

D. The function has two real zeros and a maximum.
Incorrect. This has a maximum, and the zeroes are -4 and 2 which are real rational numbers.

Which graph below shows the critical points of the function indicated by the data in the table?

A
Incorrect. This function has been shrunk vertically.

B
Correct! All the points can be matched with coordinates in the table.

C
Incorrect. Check the x-values carefully.

D
Incorrect. This one doesn’t have any points that match.

The following table can be modeled by which equation in factored form?

1. (x + 5)(x + 1)
2. (x + 5)x
3. -(x + 5)(x + 1)
4. -(x + 5)x

A
Correct! Zeros at -5 and -1 and parabola opens upward.

B
Incorrect. The x-intercepts here should be -5 and 0.

C
Incorrect. Zeros are in the right place, but parabola opens downward.

D
Incorrect. This one opens downward, not upward.

Which of the following equations below models the values in the table?

1. y = 1 2 (x + 2)² − 5
2. y = 1 2 (x − 2)² + 5
3. y = 1 2 (x + 5)² − 2
4. y = 1 2 (x − 5)² + 2

A
Correct! The vertex is (-2, -5) and the parabola will open upward.

B
Incorrect. In this one h = 2 and k = 5, vertex (2, 5).

C
Incorrect. This one has h = -5 and k = -2, vertex (-5, -2).

D
Incorrect. This one has h = 5 and k = 2, vertex (5, 2).