Question

A graph of a slope facing to the right, with coordinate points of (0, -1) (1, 0) and (2, 2)

What transformations on the parent function have occurred?

Create an equation for the function shown on the graph: f (x) = _____

Answer 1

Those three points fit a quadratic. Solving gives

f(x) = (1/2)x^2 + (1/2)x − 1.

In vertex form this is
f(x) = (1/2)(x + 1/2)^2 − 9/8.

So, relative to the parent f(x) = x^2 the graph is:
- horizontally shifted left 1/2,
- vertically shrunk by a factor of 1/2 (multiplied by 1/2),
- vertically shifted down 9/8.