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

• A. $(-5,-1)$
• B. $(-5,-5)$
• C. $(-1,-3)$
• D. $(-2,-3)$

Answer 1

The correct option is A $(-5,-1)$

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

Complete square and determine vertex as:

$y=(2x^2+4x+4)-8+5=2{(x+2)}^2-3$ 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 right and $2$ units up.

Vertex after translations is at $(-2-3,-3+2)=(-5,-1)$.

Hence, option A is correct.