# 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]}