Question

Create a graph; then answer the following question.

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

(1 point)
Responses

x-intercept: (0,8)

y-intercept: (0,0)

vertex: (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-intercept: (4,−16)

y-intercept: (0,0)

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

vertex: (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) (8,0)

y-intercept: (0,0)

vertex: (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

Answer 1

To analyze the function \( y = x^2 - 8x \), we can rewrite it in vertex form by completing the square.

1. **Vertex Form**:
\[
y = x^2 - 8x
\]
To complete the square:
\[
y = (x^2 - 8x + 16) - 16 = (x - 4)^2 - 16
\]
The vertex is at the point \((4, -16)\).

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

3. **Y-intercept**:
To find the y-intercept, set \( x = 0 \):
\[
y = 0^2 - 8(0) = 0
\]
So 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 these findings, the correct response from the multiple-choice given would be:

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