Determine the standard form of an equation of the parabola subject to the given conditions.

Question

Vertex:(-3, -1) ; passes through  (9, 11)

Answer 1

if it's an upward opening parabola then

y=a(x+3)^2 -1

11=a(9+3)^2 -1

11=144a =1

144a = 10

a = 10/144 = 5/72

y = (5/72)(x+3)^2 -1 or

72y = 5(x+3)^2 -72

but if it's a rightward opening parabola, then

x=a(y+1)^2 -3

9=a(11+1)^2 -3

9+3 = 144a

a = 12/144 = 1/12

x = (1/12)(y+1)^2 -3

or

12x = (y+1)^2 - 36

Given the vertex and the point, the parabola could be either of the above.

Actually there's an infinite number of parabolas and equations that could describe a vertex of (-3,-1) with the point (9,11), but all those are at angles other than upward or rightward opening parabolas. They're all at diagonal or inbetween angles.

Odds are you want the upward opening parabola. It's the most standard.