The function f(x) = –x^2 + 60x – 116 models the monthly profit, in dollars, a shop makes for repairing windshields, where x is the number of windshields repaired, and f(x) is the amount of profit.
Part A: Determine the vertex. What does this calculation mean in the context of the problem? (5 points)
Part B: Determine the x-intercepts. What do these values mean in the context of the problem? (5 points)
f(x)=y=-x^2+60x-116 y+116=-x^2+60x y+116=-1(x^2-60x) y+116-900=-1(x^2-60x+900) y-784=-1(x-30)^2 y=-1(x-30)^2+784 we know that h=-b/2a h=-60/(-2*1) h=30 k=-30^2+60(30)-116 k=784
the vertex is at (30,784) this means that the point of symmetry of the parabola is at (30,784), in our context it means that the maximum number of windshields repaired is 30 and the minimum profit will be $784
Part B x-intercept to determine the x-intercept we let f(x)=0 thus 0=-2x^2+60x-116 solving for x we get: x=2 and x=58 this means that when the shop repairs 2 windshields or 58 windshields, they will not make any profits
