Graph the function f(x)=2x^2−2x
. What is the y-value that corresponds to the x-value of −1
?(1 point)
We have the quadratic function f(x)=2x^2−2x.
To find the y-value that corresponds to the x-value of -1, we simply substitute x with -1 into the function:
f(-1) = 2(-1)^2 - 2(-1)
= 2(1) + 2
= 2 + 2
= 4
So, the y-value corresponding to the x-value of -1 is 4.
Now, let's give you an idea of the graph of this function. Since it's a quadratic function, it will be a parabola. The coefficient of x^2 is positive (2), so the parabola will open upwards. This parabola has its vertex on the line of symmetry which can be found using the formula -b/(2a) for the x-coordinate of the vertex:
x = -(-2) / (2*2)
x = 2 / 4
x = 1/2
And we find the y-coordinate of the vertex by plugging x = 1/2 into the function:
f(1/2) = 2(1/2)^2 - 2(1/2)
= 2 * 1/4 - 1
= 1/2 - 1
= -1/2
So the vertex of the parabola is at (1/2, -1/2).
If we were to draw the graph, it would be a parabola opening upwards with the vertex at the point (1/2, -1/2). It intersects the y-axis at the point where x = 0, which would be:
f(0) = 2*0^2 - 2*0
= 0 - 0
= 0
So, the graph intersects the y-axis at (0,0), and for our particular point of interest at x = -1, the graph would pass through the point (-1,4).