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-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-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-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-intercept: (4,−16)

y-intercept: (0,0)

vertex: (8,0)

Answer 1

To analyze the quadratic function \( y = x^2 - 8x \), we can identify the key points: the vertex, x-intercepts, and y-intercept.

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

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

Now, substitute \( x = 4 \) back into the original equation to find \( y \):
\[
y = (4)^2 - 8(4) = 16 - 32 = -16
\]

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

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

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

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

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 the analysis above, the correct response from your options would be:
- **x-intercepts:** (0,0) and (8,0)
- **y-intercept:** (0,0)
- **vertex:** (4,−16)