Question

Graph the functions f(x)=−x3+3x2 and g(x)=−x4+5x3−6x2+3 using a graphing tool, such as the one provided here.

What is/are the approximate solution(s) of the system containing f(x) and g(x)?

There may be more than one correct answer. Select all correct answers.

(3.5,−6.05)
(0.78,1.35)
(2.22,3.84)
(0.5,−0.86)
(−0.74,2.04)
(−0.5,0.86)
(1.38,8.34)
(0.67,1.62)

I believe for f(x) it is (0.67,1.62) am I correct and if so I need help finding g(x). Thank you

Answer 1

In this format, we write powers like this:
f(x) = −x^3+3x^2, g(x) = −x^4+5x^3−6x^2+3

I plotted your functions and got this:
https://www.wolframalpha.com/input/?i=plot+y+%3D+%E2%88%92x%5E3%2B3x%5E2%2C+y+%3D%E2%88%92x%5E4%2B5x%5E3%E2%88%926x%5E2%2B3+from+-1+to+4