Asked by Gucci$harma
the function -2x^2+16x+40 represents the area of a rectangle. plz explain wat x standa for if y is the area of the rectangle and tell me what is the domain and range and why. thanks ;)
Answers
Answered by
Damon
Lets complete the square to look at the parabola
y = -2x^2+16x+40
x^2 - 8 x -20 = -y/2
x^2 - 8 x = -y/2 + 20
x^2 - 8 x + 16 = -y/2 +36
(x-4)^2 = -(1/2)(y-72)
so max area occurs when x = 4 and area = 72
zeros are when x^2-8x-20 = 0
(x-10)(x+2) = 0
or
when x = 10 and when x = -2
so
area is negative if x<-2 or if x>10
so
domain from x = -2 to x = +10
range from 0 to 72
y = -2x^2+16x+40
x^2 - 8 x -20 = -y/2
x^2 - 8 x = -y/2 + 20
x^2 - 8 x + 16 = -y/2 +36
(x-4)^2 = -(1/2)(y-72)
so max area occurs when x = 4 and area = 72
zeros are when x^2-8x-20 = 0
(x-10)(x+2) = 0
or
when x = 10 and when x = -2
so
area is negative if x<-2 or if x>10
so
domain from x = -2 to x = +10
range from 0 to 72
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