Question

The graph shown below is after a transformation.

A parabola is drawn in a coordinate plane where the axes range from negative 10 to 10, both by 1-unit increments.

(2 points)
Write the parent function: y=


Write the transformed function: y=

Answer 1

I can’t see the graph you mean — please either upload the image or tell me the vertex and one other point on the parabola (or three clear points).

Meanwhile, general answers and instructions:

- Parent function: y = x^2

- Transformed function: use the vertex form
y = a(x − h)^2 + k
where (h, k) is the vertex and a is the vertical stretch/compression (a < 0 if it opens downward).

How to find a from the graph:
1. Read the vertex (h, k) from the graph.
2. Pick another point (x1, y1) on the parabola.
3. Solve a = (y1 − k) / (x1 − h)^2.
4. Substitute a, h, k into y = a(x − h)^2 + k.

Example: if vertex is (2, −3) and the parabola passes through (3, −1),
a = (−1 − (−3)) / (3 − 2)^2 = 2, so y = 2(x − 2)^2 − 3.

Give me the vertex and one other point (or upload the graph) and I’ll compute the exact transformed equation.