y=4-2x^2+1/6x^4
How to find
x and y-intercepts.
I think y=0 but I don't know how to solve for the x-intercept.
Y=4 sorry
you get the y-intercept when x=0
You get the x-intercept when y=0. So,
1/6 x^4 - 2x^2 + 4 = 0
x^4 - 12x^2 + 24 = 0
x^2 = (12±4√3)/2 = 6±2√3
So, take each of those values and get its ± square roots.
To find the x-intercepts, we need to set the value of y to zero and solve for x. When y is zero, we have the equation:
0 = 4 - 2x^2 + 1/6x^4
To solve this equation, we need to factor it if possible or use numerical methods like graphing calculator or software. However, factoring the given equation may not be easy due to the presence of the quadratic and quartic terms. Hence, I recommend using a graphing calculator or software to obtain the x-intercepts.
Here's how you can find the x-intercepts using a graphing calculator:
1. Enter the equation into the graphing calculator.
2. Set the y-axis (or the function) to zero by selecting or entering y = 0.
3. Graph or plot the equation.
4. The points where the graph intersects the x-axis are the x-intercepts. These points represent the values of x for which y is equal to zero.
By following these steps, you will be able to determine the x-intercepts of the given equation.