# How do you graph #h(x)=-x^3+5x^2-7x+3#?

##### 1 Answer

graph{-x^3+5x^2-7x+3 [-10, 10, -5, 5]}

#### Explanation:

This is a cubic function. The equation has degree 3, so it is an odd- degree polynomial.

The leading coefficient is negative, so as

In order to solve for the

The constant term is 3, so the coordinate of the

The zeroes of the function are the

List the factors of the constant term, 3: -3, -1, 1, 3

So,

Use synthetic division to determine the other factors.

Factor the quadratic polynomial using the factor theorem.

So,

Use synthetic division to determine the other factor.

The

The zero 1 has multiplicity 2, so the graph just touches the

The zero 3 has multiplicity 1, so the graph crosses the