Question

The function f(x) = -x² + 50x - 456 models the profit, in dollars, a game developer makes for selling a new game, where (x) is the number of games sold and (f(x)) is the amount of profit.

a) f(10)

b) f(25)

c) The number of games sold when the profit is maximized.

d) The value of x when f(x) = 0.

Answer 1

To find the values of the function f(x) = -x² + 50x - 456, we substitute the given values of x into the function and evaluate.

Step-by-step explanation:

To find the values of the function f(x) = -x² + 50x - 456, we substitute the given values of x into the function and evaluate:

a) f(10) = -10² + 50(10) - 456 = -100 + 500 - 456 = -56

b) f(25) = -25² + 50(25) - 456 = -625 + 1250 - 456 = 169

c) To find the number of games sold when the profit is maximized, we can use the vertex formula: x = -b/(2a). In this case, a = -1, b = 50. So, x = -50/(2(-1)) = 25. Therefore, the number of games sold when the profit is maximized is 25.

d) To find the value of x when f(x) = 0, we set the function equal to zero and solve for x: -x² + 50x - 456 = 0. Using the quadratic formula, we find two solutions: x = 7.81 and x = 42.19.