Graph Function

Your approach is done in a straightforward conventional way. Looks good.

Can you please explain the part 1 that how the values of x and y are plugged in

y = y(x) = 2^(-x) = 1/2^(x)
Using your sample values of x:

y(1) = 1/2^(1) = 1/2         ==> (1, 1/2)
y(0) = 1/2^(0) = 1/1 = 1   ==> (0,1)
y(-1) = 1/2^(-1) = 1/ (1/2) = 2 ==> (-1, 2)     // I see that you had (-1, 1/2) even though you had y=2

For part 2, you can graph the two curves, i.e., the quadratic and the straight lines, and then get an approximation of g(x).From the graphs, you can get a rough feel where the intersections of the two graphs are. Then you guess and compute g(x_guess). Then you increment and decrement x_guess by, say, 0.1, and see which g(x) is closer to -8. Now you have a new x_guess. and you modify x_guess by 0.5 in both directions to chose a new x_guess. Keep doing this until the new x_guess is the same as the previous one for the desired number of decimal places.

Thank You.