A vertical stretch is applied to the graph of y = (x – 2)^2 + 2 so that the transformed curve passes through (6, 27). The vertical stretch factor, rounded to the nearest tenth, is?

Answer 1

Let g(x) = Af(x) where A has a value that causes a vertical stretch/shrink to f(x).

Then A = g(x)/f(x).

When x = 6, A = g(6)/f(6). We know g(6) has a value of 27 because (6,27) is given.

f(6) = (6 - 2)² + 2 = 18.

So, A = 27/18 = 3/2 = 1.5.

g(x) = (3/2)[(x - 2)² + 2] = (3/2)(x - 2)² + 3

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