Curve Sketching Algorithm (determining x and y intercepts)

[strange swan]

I need to sketch a graph and in order to do that I need to solve for x and y intercepts for the function, f(x) = 18x^5-15x^3+5x. To solve for the x intercept(s), do I set the function equal to 0 and isolate for x?

This is what I have so far

0 = 18x^5-15x^3+5x
0 = x(18x^4-15x^2+5)

[bleak raft]

1. Wait patiently for a helper to come along.
2. Once someone helps you, say thank you and close the thread with: ```diff
   +close

[obtuse jungle]

So far you are correct. Try setting u = x^2, substituting u for x^2 and u^2 for x^4

[strange swan]

sorry, i just saw this. i already solved for the x and y int. but i don't think i need to do the quadratic stuff? because the function only has 1 x and y int

also, i have another question from the same problem. how would i find the critical numbers? the function is 18x^5-15x^3+5x and i found the derivative which is 90x^4-45x^2+5 and set it =equal to 0

0 = 90x^4-45x^2+5
0 = 5(18x^4-9x^2+1)

[obtuse jungle]

How do you know it only has 1 x intercept?

[obtuse jungle]

Same thing I told you for last one

[strange swan]

aren't the rest imaginary solutions?

[obtuse jungle]

You won’t know that till you try solving the function

[strange swan]

also, im supposed to graph this so i put it into desmos to see what it looks like

[strange swan]

+close