What is the correct standard form of the equation of the parabola?
Enter your answer below. Be sure to show each step of your work.

Step-by-step explanation:

The vertex is located at (h, k) = (-3, 3). The focus is 1 unit below the vertex so that distance (p) is -1.

The equation can be written in vertex form as ...

  y = 1/(4p)(x -h)^2 +k

Filling in the values from above, this becomes ...

  y = -1/4(x +3)^2 +3

  y = -1/4(x^2 +6x +9) +3 . . . . . . expand the square

  y = -1/4x^2 -6/4x -9/4 +3 . . . . eliminate parentheses

  y = -1/4x^2 -3/2x +3/4 . . . . . . . simplify

y = -¼(x+3)² + 3

Step-by-step explanation:

y = a(x-h)² + k

(h,k) is (-3,3)

y = a(x-(-3))² + 3

y = a(x+3)² + 3

Use (1,-1) to find a

-1 = a(1+3)² + 3

-4 = 16a

a = -¼

y = -¼(x+3)² + 3

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