Write a function in any form that would match the graph shown below.

Question

coordinates are:(-5,0), (4,0), (0,-1200)

Answer 1

It's a upward opening parabola with x intercepts -5 and 4, so the line of symmetry is x=(-5+4)/2 = -1/2

the vertex has an x coordinate of -1/2, as it's on the line of symmetry

the general form of the equation is y-h=a(x-k)^2 where (k,h) is the vertex or minimum point

y-h=a(x+1/2)^2 = a(x^2 +x +1/4) = ax^2 +ax + a/4

the y intercept is h=-1200= a/4 +h

h=-a/4-1200

-1200 =a(-1/2)^2+ h = a/4 +h

y=a(x+1/2)^2 + h

0=a(4+1/2)^2 + h

0=81a/4 + h

h=-81a/4 = -a/4 -1200

81a/4 -a/4 = 1200

80a/4 = 1200

a = (4/80)1200 = 60

h=-1200-60/4 = 1215

vertex is (-1/2, 1215)

y-1215 = 60(x+1/2)^2