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given an existing function: f(x)=0.5(x-2)2+3, what transformstiins would have to be made to result in g(x)=-2(x+3)2 -1?

User Hspandher
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Answer:

  • vertical scaling by a factor of -4
  • horizontal translation 5 units left
  • vertical translation 11 units up

Explanation:

We notice that the multiplier of the squared term in f(x) is 0.5; in g(x), it is -2, so is a factor of -4 times that in f(x).

If we scale f(x) by a factor of -4, we get ...

-4f(x) = -2(x -2)² -12

In order for the squared quantity to be x+3, we have to add 5 to the value that is squared in f(x). That is, x -2 must become x +3. We have to replace x with (x+5) to do that, so ...

(x+5) -2 = x +3

The replacement of x with x+5 amounts to a translation of 5 units to the left.

We note that the added constant after our scaling changes from +3 to -12. Instead, we want it to be -1, so we must add 11 to the scaled function. That translates it upward by 11 units.

The attached graph shows the scaled and translated function g(x):

g(x) = -4f(x +5) +11

given an existing function: f(x)=0.5(x-2)2+3, what transformstiins would have to be-example-1
User Noah Gary
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