Graph the function f(x)=2x^2−2x
. What is the y-value that corresponds to the x-value of −1
?
To graph the function f(x)=2x^2−2x, we can start by finding the x-intercepts and vertex.
To find the x-intercepts, we set f(x) = 0 and solve for x:
0 = 2x^2 - 2x
0 = x(2x - 2)
x = 0 or x = 1
So the x-intercepts are (0, 0) and (1, 0).
To find the vertex, we can use the formula x = -b / 2a, where a = 2 and b = -2:
x = -(-2) / (2*2) = 1/2
Substituting x = 1/2 into the equation:
f(1/2) = 2(1/2)^2 - 2(1/2) = 1/2 - 1 = -1/2
So the vertex is (1/2, -1/2).
Now we can plot the x-intercepts and vertex on a graph:
```
y
|
| , vertex (1/2, -1/2)
|
| .
| / \
| / \
|___0_______x_______________
```
To find the y-value that corresponds to the x-value of -1, we substitute x = -1 into the equation:
f(-1) = 2(-1)^2 - 2(-1) = 2 - (-2) = 4
So the y-value that corresponds to the x-value of -1 is 4.