Question

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

The curve is a parabola opening to the right (a "sideways" parabola) with vertex at (-2/3, 0).

Equation in sideways (standard) form:
x = (2/3) y^2 - 2/3.

If you prefer y as a function of x (two branches):
y = ± sqrt((3/2)(x + 2/3)), with domain x ≥ -2/3.
(If you must give a single f(x) choose the top branch:
f(x) = sqrt((3/2)(x + 2/3)).)

Transformations (starting from the parent y = ±√x):
- Shift left by 2/3,
- Vertical stretch by factor sqrt(3/2) (equivalently the sideways parabola has coefficient 2/3 and vertex (-2/3,0)).