Given : f(x) = -x^2 + 2x + 5
Calculate f(-3) - f (2)
To calculate f(-3) we substitute -3 into the function and solve:
f(-3) = -(-3)^2 + 2(-3) + 5
f(-3) = -9 - 6 + 5
f(-3) = -10
Next, we calculate f(2):
f(2) = -(2)^2 + 2(2) + 5
f(2) = -4 + 4 + 5
f(2) = 5
Now we can calculate f(-3) - f(2):
f(-3) - f(2) = -10 - 5
f(-3) - f(2) = -15
Therefore, f(-3) - f(2) equals -15.