How do you sketch #2x^4-x^2+5#?
1 Answer
Mar 30, 2018
See explanation...
Explanation:
Given:
#f(x) = 2x^4-x^2+5#
Complete the square as follows:
#f(x) = 1/8(16x^4-8x^2+1)+39/8#
#color(white)(f(x)) = 1/8(4x^2-1)^2+39/8#
#color(white)(f(x)) = 1/8(2x-1)^2(2x+1)^2+39/8#
So
Also note that
Since all of the terms of
So this quartic is a classic "W" shape, with turning points at
If we want any more guidance, we can just evaluate
graph{2x^4-x^2+5 [-2.508, 2.492, 3.72, 6.22]}