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.

Answer 1

Parent (standard) function: y = x^2.

Transformations: the parabola is reflected across the x‑axis (no horizontal or vertical shift, no vertical stretch or compression).

Equation: using vertex form y = a(x − h)^2 + k with vertex (h,k) = (0,0) gives y = ax^2. Use (1, −1): −1 = a(1)^2 ⇒ a = −1. So the equation is

y = −x^2,

which indeed gives (±1, −1) and (±2, −4).