How do i find the vertex of a parabola given 2 points and the focus, but no vertex?

Question

I have that it passes through the points (±2, 7) and (±1, 5). and that it has focus at (0,7), but nothing else

Answer 1

One way...

Y=Ax^2+bx+c

(1,5) --> a+b+c=5

(-1,5) --> a-b+c=5

(2,7) --> 4a+2b+c=7

Subtracting the first two equations:

2b=0 --> b=0

Then a+c=5

4a+c=7

Subtracting... 3a=2--> a=2/3

C=13/3

(2/3)x^2+(13/3)=y

Completes the square to find vertex