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

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

vertex: (4,−16)
(
4
,
−
16
)

x -intercepts: left parenthesis 0 comma 0 right parenthesis left parenthesis 8 comma 0 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-intercept: (4,−16)
(
4
,
−
16
)

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

vertex: (8,0)

Answer 1

To analyze the quadratic function \( y = x^2 - 8x \), let's first identify its key points: the vertex, x-intercept(s), and y-intercept.

### 1. Finding the vertex:
The vertex of a quadratic function in standard form \( y = ax^2 + bx + c \) can be found using the formula for the x-coordinate:

\[
x = -\frac{b}{2a}
\]

Here, \( a = 1 \) and \( b = -8 \), so:

\[
x = -\frac{-8}{2 \cdot 1} = \frac{8}{2} = 4
\]

To find the y-coordinate of the vertex, substitute \( x = 4 \) back into the function:

\[
y = (4)^2 - 8 \cdot 4 = 16 - 32 = -16
\]

Thus, the vertex is \( (4, -16) \).

### 2. Finding the x-intercepts:
To find the x-intercepts, set \( y = 0 \):

\[
0 = x^2 - 8x
\]

Factoring gives:

\[
0 = x(x - 8)
\]

The solutions are:

\[
x = 0 \quad \text{and} \quad x = 8
\]

Thus, the x-intercepts are \( (0, 0) \) and \( (8, 0) \).

### 3. Finding the y-intercept:
To find the y-intercept, set \( x = 0 \):

\[
y = 0^2 - 8 \cdot 0 = 0
\]

Thus, the y-intercept is \( (0, 0) \).

### Summary of Key Points:
- **Vertex**: \( (4, -16) \)
- **x-intercepts**: \( (0, 0) \), \( (8, 0) \)
- **y-intercept**: \( (0, 0) \)

### Conclusion:
Based on the above analysis, the correct response is:

**x-intercepts**: \( (0, 0) \), \( (8, 0) \)
**y-intercept**: \( (0, 0) \)
**vertex**: \( (4, -16) \)

Therefore, the correct option from your choices is:

**x-intercepts: (0,0) (8,0)**, **y-intercept: (0,0)**, **vertex: (4,−16)**.