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: (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
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Answer 1

To analyze the function \( y = x^2 - 8x \), we can find the key points:

1. Vertex: The vertex of a quadratic function in the form \( y = ax^2 + bx + c \) can be found using the formula \( x = -\frac{b}{2a} \). Here, \( a = 1 \) and \( b = -8 \).

   \[ x = -\frac{-8}{2 \cdot 1} = \frac{8}{2} = 4 \]

   To find the y-coordinate of the vertex, we substitute \( x = 4 \) back into the original equation:

   \[ y = (4)^2 - 8(4) = 16 - 32 = -16 \]

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

2. X-intercepts: To find the x-intercepts, set \( y = 0 \):

   \[ 0 = x^2 - 8x \]

   Factor the equation:

   \[ 0 = x(x - 8) \]

   The solutions are \( x = 0 \) and \( x = 8 \). 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: \( (0, 0) \)

Conclusion:

The correct option from the choices provided is:

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