Question

I need the parent function and the transformation with some explanation, thank you.

Answer 1

• parent: y = x²
• transformed: y = -3x² +4

Explanation:

You have correctly recognized that the function is quadratic, so has parent function y = x².

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You may notice that the function drops by 3 units when x increases or decreases by 1 unit from the vertex. That factor (-3) is the vertical scale factor in the transformed function ...

f(x) = a(x -h)² +k

where "a" is the vertical scale factor and (h, k) is the location of the vertex of the transformed function.

We note that the graphed function has its vertex at (h, k) = (0, 4), so the complete transformed function with a=-3, h=0, k=4 is ...

f(x) = -3x² +4