Can You Find X And Y Intercepts Of X^4 - 8x^2 - 9?

You appear to be interested in the equation
y = x⁴ - 8x² - 9

This factors as
y = (x²+1)(x²-9) = (x²+1)(x-3)(x+3)

It has x intercepts of x = {-3, +3} and a y intercept of -9.