Writing the Quadratic Function Using a Graph

There are instances when you may be given a graph instead of the roots and a vertex. Remember, you can find the roots of a function along with the vertex right on the graph.

Suppose you have the following graph and are asked to write the equation of the quadratic.

Graph of quadratic function with zeros at x = -3 and 1, and
vertex at (-1, -8).

We can see from the graph that the roots of the function are -3 and 1 and the vertex is (-1, -8). You can use this information to write the quadratic. Work through this problem and check your answer.
 

What is the equation of the quadratic function with roots -3 and 1 and a vertex a
(-1, -8).
 

f(x) = 2x² + 4x – 6