in function notation, we get that the transformed function is:
g(x) = -2*f(x - 10) + 800
How to identify the transformation?
Here the parent function is:
f(x) = x^2
And the transformed function is the one graphed in the lower right side of the given image.
Notice that the y-intercept of the transformed function is y = 600.
The x-intercepts are x = -10 and x = 30
Then the polynomial is something like:
y = a*(x + 10)*(x - 30)
Using the fact that the y-intercept is y = 600, then:
600 = a*(0 + 10)*(0 - 30) = a*-300
600/-300 = a = -2
The transformed function is:
g(x) = -2*(x + 10)*(x - 30)
Expanding that:
g(x) = -2( x^2 + 10x - 30x - 300)
Completing squares we get:
g(x) = -2*( x^2 - 20x - 300)
= -2*(x^2 - 2*10*x - 300)
Now we can add and subtract 100, so we get:
-2*(x^2 - 2*10*x - 300 + 100 - 100)
-2*( (x - 10)^2 - 400)
Finally, expanding that:
g(x) = -2*(x - 10)^2 + 800
Writing it in function notation, we get that the transformed function is:
g(x) = -2*f(x - 10) + 800
If you want to learn more about transformations:
https://brainly.com/question/4289712
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