Question

when a parabola represented by the equation y-2(x*x)=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 = 8 x + 5 as

y = 2x^2 + 8 x + 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 right and 2 units up .

vertex after translations is at: (-2 - 3 , - 3 + 2) = (-5 , -1)