how do i graph y=x5 – 5x3 + 4x with the first x being to the 5th power and the second x to the 3rd power didnt know how to type it like that

Question

y=x⁵- 5x³ + 4x  

 

It says to use a graphing utility to graph the function. use the graph to approximate any x-intercepts of the graph. set y=0 and solve the resulting equation compare the results with any x intercepts on the graph...

Answer 1

Hi Joseph;

I do not have a graphing calculator.  I can offer the following with the hope that it helps...

y=x⁵- 5x³ + 4x

y=0

0=x(x⁴-5x²+4)

x=0 is one solution.

Let's take x⁴-5x²+4 and factor...

0=(x²-1)(x²-4)

Either parenthetical equation may equal zero.

0=x²-1

x=1 is another solution.

and

0=x²-4

x=2 is another solution.

 

When y=0, then x=0, 1, 2