Question

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

Answer 1

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 =
`(1)/(2)`

Therefore,
`g(x)=(1)/(2)[p(x)]`

Which shows a horizontal stretch of the function 'p' by a scale factor of
`(1)/(2)`.