Write an equation in vertex or intercept form as appropriate for each graph or given information

Question

Vertex (-4,3) and through the point (2,-15)

Answer 1

Starting with the parent function"

y=x² Plug in the vertex

(y-3) = (x-(-4))² Simplify

(y-3) = (x+4)² To make it go through the correct point, need to figure out if there is a vertical stretch

(y-3) = a(x+4)² Plug in the point it goes through, solve for a

(-15-3) = a(2+4)² Simplify

-18 = 36a Divide by 36

a=-1/2 Plug in a

(y-3) = -1/2(x+4)²

Answer 2

The standard vertex form for a parabola is

y -= a(x - h)^2 + k where h,k are the coordinates of the vertex. a is obtained by substituting the vertex

coordinates for h and k and letting y = -15 when x =2 and solving for a.

y = a(x - (-4))^2 + 3 = a(x +4)^2 +3

-15 = a(2 +4)^2 +3

-15 = a*36 +3

a = -18/36 = -1/2

The equation becomes

y = -1/2(x + 4)^2 +3