What is the standard form of the parabola with the points of (-1,4) (0,5) and (1,8)

Question

I have the graph but I need to put it into standard form of the parabola

Answer 1

y=ax^2+bx+c is one form representing a parabola.

Plug in (0,5): 5=c, y=ax^2+bx+5.

Plug in (-1,4): 4=a-b+5, so b-a=1 or b=a+1.

Plug in (1,8): 8=a+b+5=2a+6, 2a=2, a=1, b=2, y=x^2+2x+5=(x+1)^2+4 or (y-4)=(x+1)^2 which shows the vertex to be at (-1,4) and the parabola is U-shaped.