how to write y=x^2 when is compressed vertically by a factor of 5, reflected across the x -axis, and then translated left 4 units, and up 3 units

Question

I'm not sure what vertically compressed by a factor of 5 means, I know vertically stretched by a factor of 5, and vertically compressed by a factor of 1/5 but not by 5. Thank you.

Answer 1

y=x^2

compressed by a factor of 5 is

y=(1/5)x^2 = x^2/5

the upward opening parabola gets flattened quite a bit

then vertically stretched by a factor of 5 to go back where you started

y = x^2/5 times 5 = x^2 but the bold face question doesn't say that. Instead it goes from y=x^2/5 to reflection across the x axis which changes y to -y, thus -y = x^2/5 or y = -x^2/5

translated 4 left means y=-(x+4)^2/5

then translated up 3: y=-(x+4)^2/5 + 3