Maths - Parabola Equations

Hey guys! I'm new here & browse more thanb I post

I have an emergency, and a lot of guys who are here are pretty knowledgable.

If you could help me out with my question below I would be so happy! Thanks in advance,

Damien.

Question:

I need the EQUATION of a PARABOLA in the form of y = ax^2 + bx + c

I have three points; A (17, 3), B (51,3) and C (34, z)

Z is unkown, however, point C is a local minimum.

So y' = 2ax + b

I need the EQUATION of a PARABOLA in the form of y = ax^2 + bx + c

I have three points; A (17, 3), B (51,3) and C (34, z)

Z is unkown, however, point C is a local minimum.

So y' = 2ax + b. Can anyone help me find the equation of the parabola and the value of z?