Question

question 14 of 40
which transformations, when performed together, would carry graph a onto graph b? choose all that apply.
(graphs of a and b are shown, with a being a parabola opening upwards and b a parabola opening downwards, along with grid lines and axes. options: a. a vertical compression with a scale factor of 1/2; b. a reflection over the x - axis; c. a vertical stretch with a scale factor of 2; d. a translation of 4 units up)

Explanation:

Step1: Analyze vertex positions

Graph A's vertex is at (0,0); Graph B's vertex is at (0,4). The difference is +4, so translation up 4 units.

Step2: Analyze vertical scale

Graph A’s arms go to high y-values; Graph B’s arms go to lower y-values. A vertical compression by 1/2 reduces height, matching B’s scale.

Step3: Check reflection

Graphs A and B are both downward-opening, so no x-axis reflection.

Answer:

A. A vertical compression with a scale factor of 1/2, D. A translation of 4 units up