Compressed by a factor of 1/2, horizontally and
vertically translated 5 units

can someone help me find the equation

I think your talking about quadratics, so

They didn’t specify which way the parabola was translated, right or left, up or down?

Since there wasn’t specification of direction, I will use positive (to the right) and up (upwards)

a = 1/2
h = +5
k = +5

y = a(x-h)^2+k
y = 1/2 (x - 5)^2 + 5

Now if your writing it in standard form (above was vertex form) you’d just expand it

y = 1/2 (x-5)(x-5) + 5
y = 1/2 [(x^2) -5x -5x ] + 25 + 5
y = 1/2 x^2 - 5x + 30