Select all the transformations of f(x) = x2 that combine to result in the graph of function g below.

Step-by-step explanation:

Parent function for the given graph is,

f(x) = x²

1). When the given function is inverted or reflected across x-axis,

  h(x) = -ax² [Since parabola is opening downwards]

2). Further the given graph is shifted 1 units left horizontally and 2 units down.

  p(x) = -a(x + 1)² - 2

  Therefore, there is a translation of 1 units towards left and 2 units down.

3). Since, the transformed function passes through (1, -4).

   p(1) = -a(1 + 1)²- 2

   -4 = -a(2)² - 2

   -4 = -4a - 2

   4a = 2

   a =

   Therefore,

  Which shows a horizontal stretch of the function 'p' by a scale factor of .

the ratio of balloons to tables is 5: 2 and the constant variation is 5.

the equation is y=5x