Features of Graphs of Quadratic Equations Quick Check

Question

4 of 54 of 5 Items
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: (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.

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 equation \( y = x^2 - 8x \), we can determine its key features such as the vertex, x-intercepts, and y-intercept.

1. Vertex: To find the vertex of the quadratic equation, we can use the vertex formula \( x = -\frac{b}{2a} \) where \( a = 1 \) and \( b = -8 \).

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

   Now, we substitute \( x = 4 \) back into the equation to find \( y \):

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

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

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

   \[ 0 = x^2 - 8x \] Factoring gives us:

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

   This gives us two x-intercepts:

   \[ x = 0 \quad \text{and} \quad x = 8 \]

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

3. Y-intercept: To find the y-intercept, we 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: \( (0, 0) \)

Responses to Choose From

The correct features you can choose from the options provided are:

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

Make sure to select the option that accurately represents this information!