# How do you graph by using the zeros for f(x)=3x^3-15x^2+18x?

Feb 23, 2017

You're going to have to factor to find the zeroes.

$0 = 3 {x}^{3} - 15 {x}^{2} + 18 x$

Extract a common factor $3 x$.

$0 = 3 x \left({x}^{2} - 5 x + 6\right)$

$0 = 3 x \left(x - 3\right) \left(x - 2\right)$

$x = 0 , 3 \mathmr{and} 2$

Now use properties of polynomial functions to determine the end behavior.

When you get more advanced in mathematics, you may use calculus to draw a more precise graph. But for the sake of this answer, I won't go into that. Here is the graph.

graph{3x^3 - 15x^2 + 18x [-10, 10, -5, 5]}

Hopefully this helps!