Question

Write and equation of the translated or rotated graph in general form

Answer 1

$(x+3)^2 =4 y$

That's a parabola, almost in vertex form:

$y = \frac 1 4 (x+3)^2$

The translation is

$(x',y') = T_{(-7,2)} (x,y) = (x-7, y+2)$

$x= x'+7, y=y'-2$

Substituting translates the graph. None of the choices have fractions so we substitute into the original form:

$(x'+7+3)^2=4(y'-2)$

We can drop the primes now and simplify,

$(x+10)^2=4(y-2)$

$x^2 + 20 x + 100 = 4y -8$

$x^2 + 20 x - 4y + 108 = 0$

Choice C.

This method generalizes nicely to rotations, reflections and other transformations.