Question

Create a graph; then answer the following question.

What are the key points on the graph of y=x2−8x
y
=
x
2
−
8
x
? Name the vertex, x-intercept(s), and y-intercept.

(1 point)
Responses

x-intercept: (4,−16)
(
4
,
−
16
)

y-intercept: (0,0)
(
0
,
0
)

vertex: (8,0)
(
8
,
0
)

x -intercept: left parenthesis 4 comma negative 16 right parenthesis y -intercept: left parenthesis 0 comma 0 right parenthesis vertex: left parenthesis 8 comma 0 right parenthesis

x-intercept: (0,8)
(
0
,
8
)

y-intercept: (0,0)
(
0
,
0
)

vertex: (4,−16)
(
4
,
−
16
)

x -intercept: left parenthesis 0 comma 8 right parenthesis y -intercept: left parenthesis 0 comma 0 right parenthesis vertex: left parenthesis 4 comma negative 16 right parenthesis

x-intercepts: (0,0)
(
0
,
0
)
(0,8)
(
0
,
8
)

vertex: (4,−16)
(
4
,
−
16
)

There is no y-intercept.

x -intercepts: left parenthesis 0 comma 0 right parenthesis left parenthesis 0 comma 8 right parenthesis vertex: left parenthesis 4 comma negative 16 right parenthesis There is no y -intercept.

x-intercepts: (0,0)
(
0
,
0
)
(8,0)
(
8
,
0
)

y-intercept: (0,0)
(
0
,
0
)

vertex: (4,−16)

Answer 1

To analyze the quadratic function \( y = x^2 - 8x \), we will find the vertex, x-intercepts, and y-intercept.

### 1. Vertex
The vertex of a quadratic function in the form \( y = ax^2 + bx + c \) can be calculated using the formula:
\[
x = -\frac{b}{2a}
\]

In this case, \( a = 1 \) and \( b = -8 \):
\[
x = -\frac{-8}{2 \cdot 1} = \frac{8}{2} = 4
\]

To find the y-coordinate of the vertex, substitute \( x = 4 \) into the function:
\[
y = (4)^2 - 8(4) = 16 - 32 = -16
\]

Thus, the vertex is:
\[
\text{Vertex: } (4, -16)
\]

### 2. X-Intercepts
To find the x-intercepts, set \( y = 0 \):
\[
0 = x^2 - 8x
\]
Factoring gives:
\[
0 = x(x - 8)
\]
Setting each factor to zero:
\[
x = 0 \quad \text{or} \quad x - 8 = 0 \rightarrow x = 8
\]

Thus, the x-intercepts are:
\[
\text{X-Intercepts: } (0, 0) \text{ and } (8, 0)
\]

### 3. Y-Intercept
To find the y-intercept, set \( x = 0 \):
\[
y = (0)^2 - 8(0) = 0
\]

Thus, the y-intercept is:
\[
\text{Y-Intercept: } (0, 0)
\]

### Summary of Key Points
- **Vertex:** \( (4, -16) \)
- **X-Intercepts:** \( (0, 0) \) and \( (8, 0) \)
- **Y-Intercept:** \( (0, 0) \)

### Conclusion
Now, looking at the provided options:
- The responses indicating a vertex of (4, -16) are correct.
- The x-intercepts should indeed be (0, 0) and (8, 0) with the y-intercept also being (0, 0).

Correct selection reflecting this would be:
- Vertex: (4, -16)
- X-Intercepts: (0, 0) and (8, 0)
- Y-Intercept: (0, 0)