11)
Jackie has 50 feet of fencing that he can use to make a small rectangular pen for his llamas in his backyard. He is trying to decide how long to make the pen. The quadratic function f(x)=−x2+50x
gives the area of the pen, in square feet, when he makes it x
feet long.
What are the values of f(x)
in the table below?
(4 points)
x
f(x)
5
10
15
20
To find the values of f(x) in the table, we need to substitute the given values of x into the quadratic function f(x) = -x^2 + 50x and calculate the corresponding values of f(x).
When x = 5:
f(5) = -(5)^2 + 50(5)
f(5) = -25 + 250
f(5) = 225
When x = 10:
f(10) = -(10)^2 + 50(10)
f(10) = -100 + 500
f(10) = 400
When x = 15:
f(15) = -(15)^2 + 50(15)
f(15) = -225 + 750
f(15) = 525
When x = 20:
f(20) = -(20)^2 + 50(20)
f(20) = -400 + 1000
f(20) = 600
Therefore, the values of f(x) in the table are:
x f(x)
5 225
10 400
15 525
20 600