The graph shown appears to be a cubic polynomial based on its general shape. Let me break down how to find the equation step by step:

Observations:

1. Roots (x-intercepts):

   • The graph crosses the x-axis at $x = -2$ and $x = 1$.
   • There seems to be a double root at $x = 1$ (the curve touches the x-axis and bounces back without crossing).

2. Behavior of the Graph:

   • The cubic graph suggests an odd-degree polynomial with a leading coefficient of $\pm 1$. Since the graph starts downward and ends upward, the leading coefficient is $+1$.

Constructing the Equation:

• Since the graph has a root at $x = -2$, this corresponds to the factor $(x + 2)$.
• The graph has a double root at $x = 1$, corresponding to the factor $(x - 1)^2$.

Therefore, the equation in factored form is:

$y = (x + 2)(x - 1)^2$

This is the equation of the cubic polynomial that fits the graph.

Would you like further details on how the factors correspond to the graph?

Related Questions:

1. How do you determine the degree of a polynomial from its graph?
2. What is the significance of double roots in polynomial equations?
3. How does the leading coefficient affect the shape of a cubic graph?
4. What is the difference between crossing and touching the x-axis at a root?
5. Can a cubic function have more than three real roots?

Tip:

When identifying polynomial graphs, always look for how many times the curve touches or crosses the x-axis. This helps in identifying the degree and multiplicity of roots.