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

(h, k) is the vertex

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:

(h, k) = (2, -7)a = -2              ⇒         ⇒    

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

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

2+2-9-$29: ! 3$3$282! 2! 2

both graphs increase on their domain

neither graph has a y-intercept

step-by-step explanation:

the following points can be visualized easily from the graph

there is a hike in both the graphs so the graphs are increasing on their domain.x-intercept of log x and log 6x are differentthere is a vertical asymptote of both the graphs so there is no y-interceptas both the graphs are increasing so there is no horizontal asymptote