Question

A graph of a u-shaped curve pointing upward, with coordinate points of: (-7, 4) (-6, 1) vertex (-5, 0) (-4, 1) (-3, 4)

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

First note the symmetry of the y-values shows the vertex is at (-5, 0) (points are at x = -7,-6,-5,-4,-3 symmetric about x = -5).

Transformations from the parent y = x^2:
- Horizontal translation left 5 units.
- No vertical translation, no reflection, no vertical stretch/compression (scale factor a = 1).

Equation:
f(x) = (x + 5)^2

(Checks: x = -4 → (1)^2 = 1; x = -7 → (-2)^2 = 4, etc.)