Question 1

The quadratic function  has a vertex at  .

Accepted Answer

Since the vertex of a quadratic function is always in the form of (h, k), we can determine if the statement is true by examining the given vertex. If the x-coordinate of the vertex is 11ec1b6e_3c5c_a609_bbf8_2944b326ddfd_TBX8728_11 and the y-coordinate is also 11ec1b6e_3c5c_a60a_bbf8_cba682710aee_TBX8728_11, then the statement is true. However, without knowing the exact values of the coordinates, we cannot say for certain.

Question 2

The vertex of  is  .

Accepted Answer

The vertex is the starting point of the edge, and in this case, it is 11ec1b6e_3c5c_7ef3_bbf8_5dcb35f6fae1_TBX8728_11.

Question 3

The equation  has 2 real solutions.

Accepted Answer

It is not possible to determine if an equation has real solutions without knowing the coefficients and the degree of the equation. The given equation is a string of characters and cannot be analyzed mathematically.

Question 4

is a factor of the perfect square  .

Accepted Answer

To check if 11ec1b6e_3c5d_1b45_bbf8_eb53298132c1_TBX8728_11 is a factor of the perfect square 11ec1b6e_3c5d_1b46_bbf8_37a35a8ee309_TBX8728_11, we can divide the perfect square by the potential factor:

11ec1b6e_3c5d_1b46_bbf8_37a35a8ee309_TBX8728_11 / 11ec1b6e_3c5d_1b45_bbf8_eb53298132c1_TBX8728_11 = 10000000000000000000000000000000001

As we can see, the division is exact, meaning that 11ec1b6e_3c5d_1b45_bbf8_eb53298132c1_TBX8728_11 is indeed a factor of the perfect square. Therefore, the answer is A.

Question 5

Which one of the following graphs illustrate the function  ?
A) 
B) 
C) None of these options
D) 
E)

Accepted Answer

The answer of Which one of the following graphs illustrate...

Question 6

The graph of  is obtained from the graph of  by shifting the graph left 5 units.

Accepted Answer

The answer of The graph of  is obtained from...

Question 7

The graph of  opens upward.

Accepted Answer

The answer of The graph of  opens upward....

Question 8

Which one of the following graphs illustrate the function  ?
A) 
B) 
C) None of these options
D) 
E)

Accepted Answer

The answer of Which one of the following graphs illustrate...

Question 9

The quadratic function  has a maximum value at  when  .

Accepted Answer

The answer of The quadratic function  has a maximum...

Question 10

Which one of the following functions translates the graph of  to a new graph g with a vertical shift down 3 units and a horizontal shift left 8 units.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Which one of the following functions translates...

Question 11

A function f is given by the table. Find . 
A) 3
B) -1
C) 4
D) -4
E) 0

Accepted Answer

Looking at the table, we can see that the input values are increasing by 1 each time, while the output values are decreasing by 2 each time. Therefore, to find the value of f(8), we can start with the value of f(5) and subtract 2 for each additional input value beyond 5.

f(5) = 1
f(6) = -1 (subtract 2)
f(7) = -3 (subtract 2 again)
f(8) = -5 (subtract 2 again)

Therefore, f(8) = -5, which is answer choice B).

Question 12

Which one of the following graphs illustrate the function  ?
A) 
B) 
C) None of these options
D) 
E)

Accepted Answer

The answer of Which one of the following graphs illustrate...

Question 13

The minimum value of the quadratic function  occurs when  .

Accepted Answer

True. The minimum value of a quadratic function occurs at its vertex, where the x-coordinate of the vertex is given by -b/2a.

Question 14

The quadratic function  has a maximum value at  .

Accepted Answer

The answer of The quadratic function  has a maximum...

Question 15

Which one of the following functions translates the graph of  to a new graph g with a reflection about the x -axis, a vertical stretch by a factor of 6, and a horizontal shift left 5 units.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Which one of the following functions translates...

Question 16

If the y -values of a set of data decrease by 7 for each increase of 1 in the x -values, a quadratic function may be appropriate to model the data.

Accepted Answer

A quadratic function would be appropriate if the y-values decrease by a constant square (not linear) each time the x-values increase by a constant amount. In this case, the y-values are decreasing linearly, so a quadratic function would not be appropriate.

Question 17

In the equation  , the value of a is  , the value of b is 7 and the value of c is 4.

Accepted Answer

The answer of In the equation  , the value...

Question 18

If the y -values of a set of data increase by different amounts when the x -values increase by the value of 6, then a linear function will best model the data.

Accepted Answer

A linear function implies a constant rate of change, meaning the y-values would increase by the same amount for each increase in x-values. If the y-values increase by different amounts, a non-linear function would better model the data.

Question 19

Which one of the following graphs illustrate the function  ?
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Which one of the following graphs illustrate...

Question 20

Let  and let  . If  , then the number of x -intercepts for the graph of f is 0.

Accepted Answer

The answer of Let  and let  . If...

Quiz 5: Quadratic Functions and Models

The quadratic function has a vertex at .

The vertex of is .

The equation has 2 real solutions.

is a factor of the perfect square .

Which one of the following graphs illustrate the function ?

The graph of is obtained from the graph of by shifting the graph left 5 units.

The graph of opens upward.

Which one of the following graphs illustrate the function ?

The quadratic function has a maximum value at when .

Which one of the following functions translates the graph of to a new graph g with a vertical shift down 3 units and a horizontal shift left 8 units.

A function f is given by the table. Find .

Which one of the following graphs illustrate the function ?

The minimum value of the quadratic function occurs when .

The quadratic function has a maximum value at .

Which one of the following functions translates the graph of to a new graph g with a reflection about the x -axis, a vertical stretch by a factor of 6, and a horizontal shift left 5 units.

If the y -values of a set of data decrease by 7 for each increase of 1 in the x -values, a quadratic function may be appropriate to model the data.

In the equation , the value of a is , the value of b is 7 and the value of c is 4.

If the y -values of a set of data increase by different amounts when the x -values increase by the value of 6, then a linear function will best model the data.

Which one of the following graphs illustrate the function ?

Let and let . If , then the number of x -intercepts for the graph of f is 0.