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-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: \((4,-16)\)