Question

A graph of a u-shaped curve pointing downward, with coordinate points of: vertex (0, 3) (-2, 1) (2, -1) (-3, -6) (3, -6)

What transformations on the parent function have occurred? select all that apply

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

Answer 1

Likely there is a typo in the listed point (−2,1) — the parabola with vertex (0,3) that goes through (2,−1) also goes through (−2,−1). Using the symmetric points (±3,−6) and (±2,−1) gives a consistent parabola.

Transformations from the parent f(x)=x^2:
- reflected across the x-axis (vertical reflection),
- translated up 3 units,
- no horizontal shift,
- no vertical stretch (scale factor 1 in magnitude).

Find the equation: use vertex form f(x)=a(x−0)^2+3. Plug (2,−1):
−1 = a(4)+3 → 4a = −4 → a = −1.

So f(x) = −x^2 + 3.