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) (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

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.
Skip to navigation

Answer 1

To analyze the quadratic function \( y = x^2 - 8x \), we can complete the square or use the vertex form to find the key points.

### Step 1: Find the Vertex
The function can be expressed in vertex form by completing the square:

1. Start with:
\[
y = x^2 - 8x
\]
2. To complete the square, take half of the coefficient of \( x \) (which is \(-8\)), square it, and add/subtract it within the equation:
\[
y = (x^2 - 8x + 16) - 16
\]
\[
y = (x - 4)^2 - 16
\]

The vertex of the parabola is at the point \( (4, -16) \).

### Step 2: Find the x-intercepts
The x-intercepts occur when \( y = 0 \):
\[
0 = x^2 - 8x
\]
Factoring gives:
\[
0 = x(x - 8)
\]
Thus, the x-intercepts are \( x = 0 \) and \( x = 8 \), corresponding to the points:
- \( (0, 0) \)
- \( (8, 0) \)

### Step 3: Find the y-intercept
The y-intercept occurs when \( x = 0 \):
\[
y = 0^2 - 8(0) = 0
\]
Thus, the y-intercept is:
- \( (0, 0) \)

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

### Response Selections
Based on the analysis, the correct key points are:

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

So the most accurate response would be:

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