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Find the maximum value of the function. Round to the nearest hundredth.

Find the maximum value of the function. Round to the nearest hundredth.-example-1
User Daylight
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1 Answer

4 votes

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.

User Beatrice
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