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.