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embizze eNotes educator| Certified Educator

We are given the graph of f(x) -- it looks like a parabola (but may not be one) with vertex at (4,-3) opening down.

We are given g(x)=-f(x+3)-3. Note that the graph of g(x) is the graph of f(x) translated 3 units to the left, reflected over the x-axis, and then translated 3 units down. Thus the point (4,-3) is mapped to the point (1,0) with the rest of the graph opening up.

So g(x) has one x-intercept.

As f(x) is a function (given), f(x) has 1 y-intercept.

So a=b=1 and a+b=2.

The graph and its transformation:

** Suppose that the function f(x) was f(x)=-(x-4)^2-3.

Then g(x)=-[-((x+3)-4)^2-3]-3

=-[(x-1)^2-3]-3

=-(x-1)^2+3-3

=(x-1)^2

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