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) (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)

GPT-4o mini · Answer

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)