How do you find the focus and directrix of y=-2x^2 +8x-15?

Step-by-step explanation:

First, rearrange the equation into vertex form: y = a(x - h)² + k   where

NOTE: p is the distance from the vertex to the focus

      y = -2x² + 8x - 15

y + 15 = -2x² + 8x            → added 15 to both sides

y + 15 = -2(x² - 4x)           → factored out -2 from the right side

y + 15 + (-2)(4) = -2(x² - 4x + 4)    → completed the square

y + 7 = -2(x - 2)²                → simplified

     y = -2(x - 2)² - 7           → subtracted 7 from both sides

Now it is in vertex form where:

Focus = (2, -7 + p)  →  Focus = (2, -7 + (-1/8))   →  

Directrix: y = -7 - p   →  Directrix: y = -7 - (-1/8)   →  

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step-by-step explanation: