Question

This is from the same project that I was struggling with and was similar to the other problem but I couldn't figure it out.

Answer 1

9514 1404 393

Answer:

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

Explanation:

You know that vertex form is ...

y = (1/(4p))(x -h)^2 +k

for a focus-vertex distance of p and a vertex of (h, k).

Here, the focus-vertex distance is 2-3 = -1 (difference of y-coordinates), and the vertex is (h, k) = (-3, 3). This means the vertex form equation is ...

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

Expanding the square gives ...

y = -1/4(x^2 +6x +9) +3

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

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Additional comment

The square of a binomial is ...

(x +a)^2 = x^2 +2ax +a^2