How do i find the equation of a parabola given 3 points and the axis of symmetry, but no vertex?

Question

The points that I've been given are (0,0), (-4,0), (-5,-5) and the axis of symmetry is at x=-2. That is all the info that I've been given.

Answer 1

Plot the points given with a dotted vertical line through -2 on the x-axis.

The graph appears to be opening up downward.

Since y = ax² + bx + c is one form of a parabola equation, then plug in the points to find a, b, and c

For instance (0, 0) gives 0 = a0² + b0 + c, so c = 0. That was easy!

Do the same for (-4, 0) and (-5, -5) and get 2 equations in a and b (remember that c=0)

Solve for a and b, and fill out y = ax² + bx + c.

If you need it in the vertex form, complete the square to get that.