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Find the equation of the parabola that passes through the points , , and .

There are three ways to approach this problem.

Use the -intercepts.

Notice that and are -intercepts.
What are the factors?

The equation is .
Substitute into the equation and solve for a.

Use the vertex.

Notice that since is midway between and , is the vertex.
Write the equation in vertex form.

The equation is
Substitute one of the
-intercepts into the equation and solve for .

Standard form.

Substitute the three points into the equation
to make a system of equations in three variables.

Since you know what is you can substitute it into all of the equations and solve a system of two equations in two variables.