Which equation BEST represents the graph 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. The parabola will open upward.

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

Choose the BEST verbal description of the graph of the quadratic function.

A. The function has two real, rational zeros and a minimum.
Incorrect. The zeros on the graph cannot be verified as rational and it has a maximum, not a minimum.

B. The function has two real zeros and a minimum.
Incorrect. There are two real zeros, but the graph doesn't have a minimum.

C. The function has two real, rational zeros and a maximum.
Incorrect. The zeros on the graph cannot be verified as rational.

D. The function has two real zeros and a maximum.
Correct! This parabola has two real zeros in the x-intercepts, but since they are not integers, we cannot verify from the graph that they are rational. The parabola also has a maximum point at the vertex.

Which table below shows ordered pairs of critical points on the graph?

A.
x
y
-1
7.5
0
5
1
3.5
2
3
3
3.5
4
5
5
7.5
B.
x
y
-1
12
0
7
1
4
2
3
3
4
4
7
5
12
 
C.
x
y
-5
12
-4
7
-3
4
-2
3
-1
4
0
7
1
12
D.
x
y
-5
-6
-4
-1
-3
2
-2
3
-1
2
0
-1
1
-6
 

A
Incorrect. This function has been shrink vertically.

B
Correct! All the values can be matched with points on the graph.

C
Incorrect. Check the x-values carefully.

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

The following graph 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 the parabola opens downward.

D
Incorrect. This one opens downward, not upward.