A parabola has x-axis intercepts 6 and -3, and passes through the point (1,10). Find the equation of the parabola

We know that this parabola intecepts the x-axis in 6 and -3. This means that is a vertical axis parabola. But also we know that our parabola passes through (1,10). Graphing these we conclude that is a concave down parabola

The general formula for this is:

To solve this we need to form a 3 equations system with our three points

We can solve for c in the first one

and replace in the second one and solve for b:

And replace c and b in the third equation:

Solve for a:

so b and c:

So: