Question

Find the absolute maximum value and the absolute minimum value, if any, of the function.
g(x) = -x(^2) + 2 x + 9

Answer 1

g'(x) = -2x + 2
This is zero when x = 1.
The second derivative, -2, is negative there, so g(1) is a maximum. The value there is 10.

There is no absolute minimum. The function is an upside-down parabola that goes to minus infinity at large and small x.

Answer 2

In google type:
functions graphs online

When you see list of results click on:

rechneronline.de/function-graphs/

When page be open in blue recatacangle type:

-x^2 + 2 x + 9

In Display properties set:

Range y-axis from -7 to 13

Then click option Draw

You will see graph of your function.