Find the zeros of the function and state their multiplicities y=x^4-8x^2+16 may someone explain this to me? also, i'd like if you could solve the function with the zeroes i have which are x=-2 & x=2. i tried using a calculator with these values but i don't think i was typing them in right.

I'll explain.

First of all, when people say 'find the zeros' they basically mean 'find the solutions.' The reason for calling them 'zeroes' is ACTUALLY important. It tells you WHAT a solution is.

Many people, even people who are all the way up in pre-calculus don't know this...
The solutions of a function are the points at which it crosses the x-axis.

With that being said, let's find the zeros of this function:
y=x^4-8x^2+16
First of all, we must factor it.
y=x^4-8x^2+16
Becomes...
y=(x+2)(x-2)(x+2)(x-2)

We can find the solutions by setting these equal to 0!
x+2=0, x=-2
x-2=0, x=2
x+2=0, x=-2
x-2=0, x=2

Now, those are your answers. Continue if you want to learn something interesting.

Look at the above picture of the graph. I want you to look at where the graph touches the x-axis. These are the solutions.

Now I will point out something interesting.

There are 3 ways in which a polynomial function touches the x-axis. I like to call them the...
Cross through: this is when the graph goes strait through the x-axis like a line.
Bounce: this is when the graph touches the x-axis at one point and then bounces back.
Wiggle through: this is when the graph makes a little 'wiggle' as it crosses the x-axis.

WHY am I pointing this out?
Well, the way in which the graph crosses the x-axis will tell you how many of the same factor the equation has.
Cross through: This indicates that the graph only has one factor that equals the value of the point it crosses through
Example: y=(x-2)(x-2)(x+1) this means at -1, the graph crosses strait through the x-axis.
Bounce: like in our example, a bounce indicates that there are two factors that equal the value of the point it touches.
Example: y=(x+2)(x-2)(x+2)(x-2) this means that at -2 and 2, the graph bounces off the x-axis
Wiggle: this indicates that 3 factors that equal the value of the point it crosses through
Example: y=(x+1)(x+1)(x+1)(x-2) the graph wiggles through the x-axis at -1

I hope this helps! Ty for reading:)

Google it that might work