Write an equation for the lowest-degree polynomial function, with the graph and intercepts shown in the figure. For this exercise, make the leading coefficient be 1 or -1

f(x)  = (x+1)² - 9

Step-by-step explanation:

We can start by seeing if this is a quadratic function, as that is the lowest degree polynomial possible.

The vertex form for a quadratic function is a(x-h)² + k, with the vertex being (h, k).

In this example, the leading coefficient (a) must be 1 or -1. If a is positive, the graph opens upward, and vice versa. Since the graph opens upward, a must be 1.

Our vertex in this picture is (-1, -9). We can plug those values in, along with a=1, to get

1(x-(-1))² - 9 = (x+1)² - 9

Therefore, our equation is f(x)  = (x+1)² - 9