Create a graph; then answer the following question.

To analyze the quadratic function \( y = x^2 - 8x \), we can rewrite it in vertex form or find its key points:

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

Here, \( a = 1 \) and \( b = -8 \):
\[
x = -\frac{-8}{2 \times 1} = \frac{8}{2} = 4
\]
Now, we can find the y-coordinate of the vertex by substituting \( x = 4 \) back into the equation:
\[
y = (4)^2 - 8 \cdot (4) = 16 - 32 = -16
\]
So, the vertex is at \( (4, -16) \).

2. **Finding the X-Intercepts:**
To find the x-intercepts, set \( y = 0 \):
\[
0 = x^2 - 8x
\]
Factoring gives:
\[
0 = x(x - 8)
\]
Thus, \( x = 0 \) or \( x = 8 \). Therefore, the x-intercepts are \( (0, 0) \) and \( (8, 0) \).

3. **Finding the Y-Intercept:**
The y-intercept is found by setting \( x = 0 \):
\[
y = (0)^2 - 8 \cdot (0) = 0
\]
This means the y-intercept is \( (0, 0) \).

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

Based on this analysis, the correct response from the options provided appears to be:
- **x-intercepts**: \( (0,0) \) and \( (8,0) \)
- **y-intercept**: \( (0,0) \)
- **vertex**: \( (4,-16) \)

So, the selection that matches these findings is:
**x-intercepts: (0,0) (8,0)**
**y-intercept: (0,0)**
**vertex: (4,−16)**