Answer:
Minimum value = 5.31
Explanation:
The equation f(x) = -1.8x^2 - 25x - 81.5 is in the standard form of a quadratic, whose general equation is given by:
ax^2 + bx + c = y, where:
- a, b, and c are constants.
Finding the x-coordinate of the minimum:
We can first find the x-coordinate of the maximum using the formula -b/2a, which comes from the quadratic equation.
Thus, we substitute -25 for b and -1.8 for a:
x-coordinate = -(-25) / 2(-1.8)
x-coordinate = 25 / -3.6
x-coordinate = -125/18
Finding the minimum value (i.e., the y-coordinate of the minimum):
Now, we can find the minimum value by substituting -125/18 for x in f(x):
f(-125/18) = -1.8(-125/18)^2 - 25(-125/18) - 81.5
f(-125/18) = -1.8(15625/324) + 3125/18 - 81.5
f(-125/18) = -3125/36 + 3125/18 - 81.5
f(-125/18) = 3125/36 - 81.5
f(-125/18) = 5.305555556
f(-125/18) = 5.31
Therefore, the minimum value is about 5.31.