Question

y=x^4-25

Answer 1

What do you need to do with that?

Answer 2

I cant remember how to solve for y

Answer 3

it's already solved for y

Answer 4

I know y=0 but after that I have forgotten

Answer 5

you mean you are trying to find the zeroes/roots of the function?

Answer 6

Y intercept

Answer 7

Oh ok.. The y-intercept it quite easy here. The y-intercept, by definition, is the y-value whenever x=0. So;
\(y=x^4-25\), plug in x=0:
\(y=0^4-25\)
\(y=0-25\)
\(y=-25\)

Answer 8

Oh ok then how do I solve for x

Answer 9

DO you mean finding the x-intercept, or actually re-writing the equation in terms of x?

Answer 10

Sorry the x intercept

Answer 11

So the x-intercept are the x-values when y=0: So plug in y=0:

\(0 = x^4-25\)

Now, notice that you actually have like a sort of quadratic equation... if you substitute \(u = x^2\), then you have:

\(0 = u^2 - 25\)
by the difference of squares (i.e from the formula \(x^2-a^2=(x-a)(x+a)\) ) you get:
\(0 = (u+5)(u-5)\)

Now plug back in \(u= x^2\):

\(0 = (x^2+5)(x^2-5)\)

Answer 12

Are you with me so far? (You can ask me about any step that confuses you)

Answer 13

So far

Answer 14

Thank you

Answer 15

Ok so next, similar to when you calculate quadratics and you have say \((x-4)(x+2)=0\), for this to be 0, either (x-4)=0 or (x-2)=0. Do the same here:

Either:
\(x^2+5=0\) or \(x^2-5=0\)

This means
\(x^2=-5\) or \(x^2 = 5\)

Still with me? If you can solve the rest on your own , try it, if not I can provide more help