Thread: Analyzing a graph

I need to find the X-intercepts of:

Y= 3x^4 - 6x^2 + 5/3

Thank you for any help.
I have been away from any math for over five years so a step by step would be appreciated.

Originally Posted by JDG1317

I need to find the X-intercepts of:

Y= 3x^4 - 6x^2 + 5/3

Thank you for any help.
I have been away from any math for over five years so a step by step would be appreciated.

the x-intercepts occur where y = 0. note that this function is quadratic in x^2. if you say, let k = x^2 for instance, the result is:

y = 3k^2 - 6k + 5/3

can you solve that for y = 0

I really don't even know what to do from there. Sorry for being a pain. I really should have relearned some of these skills before signing up for calc class.

Originally Posted by JDG1317

I really don't even know what to do from there. Sorry for being a pain. I really should have relearned some of these skills before signing up for calc class.

use the quadratic formula.

for a quadratic of the form the roots (that is, the solution(s) to ) are given by:



use that to solve for k. when done, replace k with x^2 and solve for x

When I used the quadratic equation I got:

k= 3 and,
k= .6

When I replaced k with X^2 I get

X= +/- sqrt(3)
X= +/- sqrt(.6)

These answers don't match up with the intercepts when I check them on the graphing calc.

Originally Posted by JDG1317

When I used the quadratic equation I got:

k= 3 and,
k= .6

When I replaced k with X^2 I get

X= +/- sqrt(3)
X= +/- sqrt(.6)

These answers don't match up with the intercepts when I check them on the graphing calc.

of course they don't match up. those answers are wrong. those are not the values for k