Question

A graph of a u-shaped curve pointing downward, with coordinate points of: Vertex, (0, 0) (-1, -1) (1, -1) (-2, -4) and (2, -4)

What transformations on the parent function have occured?

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

Answer 1

Parent (quadratic) is y = x^2. The graph is the parabola reflected across the x-axis (vertex stays at (0,0)), with no shifts or additional stretch/compression.

Use point (1, −1): −a(1)^2 = −1 ⇒ a = 1.

So the equation is f(x) = −x^2.