Question

The equation is f (x) = 4x^2 The coordinates plotted on the graph are (-2, 16) (-1, 4) the vertex being at (0, 0) (1, 4) (2, 16)

Interpret the key features on the graph, what type of transformation occurred from the parent function?

Answer 1

Key features of f(x) = 4x^2

- Vertex: (0, 0) — a minimum point.
- Axis of symmetry: x = 0 (the y‑axis).
- Opens: upward (parabola opens up).
- Intercepts: x‑intercept at 0 (double root), y‑intercept at 0.
- Given points: (±1, 4) and (±2, 16) — the y‑values are 4 times those of y = x^2.
- Domain: all real numbers.
- Range: y ≥ 0.
- Monotonicity: decreasing on (−∞, 0], increasing on [0, ∞).
- Symmetry: even function (f(−x) = f(x)).

Transformation from the parent function y = x^2
- A vertical stretch by a factor of 4 (every y‑value of y = x^2 is multiplied by 4).
- No horizontal or vertical shift, and no reflection.

You can see this in point mapping: (1,1) on y = x^2 becomes (1,4) on y = 4x^2; (2,4) becomes (2,16).