Question

PLEASE HELP ME

What is the correct standard form of the equation of the parabola?

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Answer 1

Below

Explanation:

Vertex is at (h,k) = (-3,3)

Vertex form of the parabola is then

y = a ( x - -3)^2 + 3 <======need to find 'a'

the 'P' value is the distance form the vertex to the focus (which is the same as the distance from the vertex to the directrix )

for this parabola P = 1

you should know that P = 1/(4a) so 1 = 1 / (4a) shows a = 1/4

then your parabola becomes y = 1/4 (x+3)^2 + 3 BUT 'a' needs to be modified to a negative because it is a upside down (dome-shaped) parabola so

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

or y = -1/4 x^2 - 6/4x + 3/4