Jason 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) = -x^2 + 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? Show your work.
x f (x)
5 a) 215 b) 225 c) 250 d) 275
10 a) 400 b) 450 c) 500 d) 600
15 a) 400 b) 450 c) 500 d) 525
20 a) 300 b) 500 c) 600 d) 800
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 solve for f(x).
a) For x = 5:
f(5) = -5^2 + 50*5
f(5) = -25 + 250
f(5) = 225
Therefore, the value of f(x) when x = 5 is 225, so the answer is b) 225.
b) For x = 10:
f(10) = -10^2 + 50*10
f(10) = -100 + 500
f(10) = 400
Therefore, the value of f(x) when x = 10 is 400, so the answer is a) 400.
c) For x = 15:
f(15) = -15^2 + 50*15
f(15) = -225 + 750
f(15) = 525
Therefore, the value of f(x) when x = 15 is 525, so the answer is d) 525.
d) For x = 20:
f(20) = -20^2 + 50*20
f(20) = -400 + 1000
f(20) = 600
Therefore, the value of f(x) when x = 20 is 600, so the answer is c) 600.
So, the answers are b) 225, a) 400, d) 525, c) 600.