Graph the function y = 4x4 – 8x2 + 4. which lists all of the turning points of the graph? (0, 4) (–1, 0) and (1, 0) (–1, 0), (0, 4), and (1, 0) (–4, 0), (–1, 0), (0, 4), and (1, 0)

Step-by-step explanation:

I figured this out using calculus, since it's easier to do it that way, I think, than any other way.  The function's derivative will give us the critical values of the function, and at the x values where the derivative is equal to 0 is where the function has either a max or a min value.  The derivative of the function is

If we set that equal to 0 and solve for the 3 values of x, we get

and

That means the x-values where the function has a max or a min are

x = -1, 0, 1

We will now sub those x values back into the original function to get the y-coordinate.

f(-1) = 0

f(0) = 4

f(1) = 0

So the coordinates where the function turns are (-1, 0), (0, 4). (1, 0)