Create a graph; then answer the following question.

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) (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

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-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
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Answer 1

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)