PLEASE HELP!

Identify the y-intercept and zeros of
y = x^4 - 9x^2 - 36
Algebraically

Our y-intercept is (0, -36).

Our real zeros are: (-2√3, 0) and (2√3, 0)

And our imaginary zeros are: (i√3, 0) and (-i√3, 0)

Step-by-step explanation:

We have the function:

Let's identify the y- and x-intercepts.

Y-Intercept:

To determine the y-intercept, we will substitute 0 for x and solve for y. So:

Evaluate:

Therefore, our y-intercept is at (0, -36).

X-Intercepts:

To determine our x-intercepts, we need to substitute 0 for y and solve for x. So:

Now, we can factor. Before doing so, we can make the factored easier to see by converting this into quadratic form. Let's let u=x². Then:

Substitute:

Now, let's factor. We can use -12 and 3. So:

Now, we can substitute back u:

Zero Product Property:

Solve for x in each case:

Take the square root of both sides. Since we're taking an even root, we will need plus/minus. Therefore:

Therefore, our zeros (both real and imaginary) are: (2√3, 0), (-2√3, 0), (i√3, 0), and (-i√3, 0)