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The function f(x) = −x2 + 60x − 116 models the monthly profit, in dollars, a shop makes for repairing windshields, where x is the number of windshields repaired. Determine the vertex, and explain what it means in the context of the problem. (30, 784); The vertex represents the maximum profit.
(30, 784); The vertex represents the minimum profit.
(2, 58); The vertex represents the maximum profit.
(2, 58); The vertex represents the minimum profit.

Respuesta :

julissagarcia107

Answer:

Even tho the answer is not up there but its

(30, 784); The vertex represents the maximum profit.

Step-by-step explanation:

....

facundo3141592

For the quadratic equation f(x) = -x^2 + 60x - 116, the vertex is (30, 784), and it is a maximum.

How to get the vertex?

For a general quadratic equation:

y = a*x^2 + b*x + c

The vertex is at the x-value:

h = -b/2a

To get the y-value, we evaluate the quadratic equation in h.

In our case, we have:

y = -x^2 + 60x - 116

Then:

h = -60/(2*-1) = 30

To get the y-value of the vertex, we evaluate in x = 30.

y = -(30)^2 + 60*30 - 116 = 784

And, as you can see, the leading coefficient of the quadratic equation is negative. This means that the arms open downwards, so the vertex is a maximum.

Then, concluding, the vertex is (30, 784), and it is a maximum.

If you want to learn more about quadratic equations, you can read:

https://brainly.com/question/1214333