Question

When a parabola represented by the equation $y-2x^2=8x+5$ is translated 3 units to the left and 2 units up, the new parabola has its vertex at

Answer 1

First rewrite $y-2x^2=8x+5$ as
$y=2x^2+8x+5$

Complete square and determine vertex.
$y=2(x^2+4x+4)-8+5$
$=2(x+2)2-3$
vertex at $(-2,-3)$
If parabola is translated $3$ units to the left and $2$ units up its vertex is also translated $3$ units to the left and $2$ units up .
vertex after translations is at: $(-2-3,-3+2)=(-5,-1).$