Question

I don’t really understand how to get this one :/

Answer 1

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:

brainly.com/question/4289712

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