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-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 Skip to navigation
The correct answer is:
x-intercepts: (0,0) (8,0)
y-intercept: (0,0)
vertex: (4,−16)
The correct answer is:
x-intercepts: (0,0) (8,0)
y-intercept: (0,0)
vertex: (4,−16)
To find the key points on the graph of the equation y = x^2 - 8x, you can plot the graph and analyze it. Let's find the x-intercepts first.
To find the x-intercepts, set y = 0 in the equation and solve for x:
0 = x^2 - 8x
To factorize this quadratic equation, we notice that x^2 - 8x can be rewritten as x(x - 8). So, we have:
0 = x(x - 8)
Setting each factor equal to zero, we get:
x = 0 and x - 8 = 0
This gives us two x-intercepts: (0, 0) and (8, 0).
Next, let's find the vertex using the formula:
x = -b/2a
In the equation y = x^2 - 8x, a = 1 and b = -8.
Substituting these values, we can find the x-coordinate of the vertex:
x = -(-8)/(2*1)
x = 8/2
x = 4
Now plug the x-coordinate of the vertex back into the equation to find the y-coordinate:
y = (4)^2 - 8(4)
y = 16 - 32
y = -16
So, the vertex is (4, -16).
Lastly, let's find the y-intercept by setting x = 0 in the equation:
y = (0)^2 - 8(0)
y = 0 - 0
y = 0
Therefore, the graph does have a y-intercept, which is (0, 0).
In conclusion, the key points on the graph of y = x^2 - 8x are:
- x-intercepts: (0, 0) and (8, 0)
- vertex: (4, -16)
- y-intercept: (0, 0)