1. ## 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.

2. 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

3. 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.

4. 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.

for a quadratic of the form $y = ax^2 + bx + c$ the roots (that is, the solution(s) to $ax^2 + bx + c = 0$) are given by:

$x = \frac {-b \pm \sqrt{b^2 - 4ac}}{2a}$

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

5. 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.

6. 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