Need help with this question, don't get it.

Given the relation x^2+3x=y^2-2y, what is the new relation if it has undergone:

A. vertical expansion by 2
B. Horizontal expansion by 3
C. Vertical compression by 4/5
D. Horizontal compression by 1/5
E. Reflection over yaxis, vertical expansion by 5 and a horizontal expansion by 9

I only get the basic stuff like:

Given the function y=f(x) what transformation occurs if

A. y is replaced with 2y. I get that, that would be a vertical compression by 1/2. But the question above I just don't get it, could someone please explain and simplify every step so I can understand?

To understand the transformations in the given question, it's important to know the effects of each transformation on a general quadratic equation of the form y = ax^2 + bx + c.

A quadratic equation in this format represents a parabola. The transformations mentioned in the question modify this parabolic shape.

Let's go through each option step by step:

A. Vertical expansion by 2:
To vertically expand a function, you multiply the entire equation by a constant. In this case, multiplying both sides of the equation by 2 gives:
2(x^2 + 3x) = 2(y^2 - 2y)
This simplifies to:
2x^2 + 6x = 2y^2 - 4y

B. Horizontal expansion by 3:
To horizontally expand a function, you replace x with (1/k)x, where k is the factor of expansion. In this case, replacing x with (1/3)x gives:
(1/3)x^2 + x = y^2 - 2y

C. Vertical compression by 4/5:
To vertically compress a function, you divide the entire equation by a constant. In this case, dividing both sides of the equation by (4/5) gives:
(5/4)(x^2 + 3x) = (5/4)(y^2 - 2y)
This simplifies to:
(5/4)x^2 + (15/4)x = (5/4)y^2 - (10/4)y

D. Horizontal compression by 1/5:
To horizontally compress a function, you replace x with kx, where k is the reciprocal of the factor of compression. In this case, replacing x with 5x gives:
(5x)^2 + 3(5x) = y^2 - 2y
This simplifies to:
25x^2 + 15x = y^2 - 2y

E. Reflection over y-axis, vertical expansion by 5, and horizontal expansion by 9:
To reflect a function over the y-axis, you replace x with -x. To apply a vertical expansion, you multiply the equation by a constant. And finally, to apply a horizontal expansion, you replace x with (1/k)x. Combining all these transformations, the equation becomes:
9(-x^2 - 3x) = 5(-y^2 + 2y)
This simplifies to:
-9x^2 - 27x = -5y^2 + 10y

Remember, these transformed equations represent new parabolic shapes resulting from the applied transformations.