Question

what transformation of y=x^2 is represented by the function -x^2 +3?

Answer 1

if you take y = x^2, and make it y = -x^2, that means you're making every point on the parabola with a certain y value have the negative of that y value.

so (1,1) becomes (1,-1)
and (2,4) becomes (2,-4)

this is pretty much creating a mirror image, and the line of symmetry will be the line y =0, or the x-axis

Answer 2

then, when you take -x^2 and make it -x^2 + 3, you're t aking each mirrored point and adding 3 to the y value

so (1,1) becomes (1,-1) which becomes (1,2)
(2,4) becomes (2,-4) which becomes (2,-1)

overall, you're reflecting each point in the x-axis, and each point is being shifted 3 units upwards

Answer 3

for example y = -e^x - 6 is taking each point on the graph of y = e^x, reflecting it in the x-axis and shifting it 6 units downwards