The function y = –3(x – 2)2 + 6 shows the daily profit (in hundreds of dollars) of a hot dog stand, where x is the price of a hot dog (in dollars). Find and interpret the zeros of this tion A. Zeros at x = 2 and x = 6 B. Zeros at C. The zeros are the hot dog prices that give $0.00 profit (no profit). D. The zeros are the hot dog prices at which they sell 0 hot dogs.
Accepted Solution
A:
the zeroes
the serose of the x value is where y=0, that is where profit=0
the zeroes of the y value is where x=0 that's when the price is 0 dollars
ok x zeroes solve for when y=0 [tex]0=-3(x-2)^2+6[/tex] [tex]-6=-3(x-2)^2[/tex] [tex]2=(x-2)^2[/tex] [tex]+/-\sqrt{2}=x-2[/tex] [tex]2+/-\sqrt{2}=x[/tex] x zeroes at [tex]x=2+\sqrt{2}[/tex] and [tex]x=2-\sqrt{2}[/tex]
y zeroes x=0 [tex]y=-3(0-2)^2+6[/tex] [tex]y=-3(-2)^2+6[/tex] [tex]y=-3(4)+6[/tex] [tex]y=-12+6[/tex] [tex]y=-6[/tex]
the y zeroes are where they sell 0 hot dogs for 0 dollars, it is $-6 profit the x zereoes are where you make 0 profit, that occurs when you sell [tex]2+\sqrt{2}[/tex] and [tex]2-\sqrt{2}[/tex] hot dogs not sure which answer you want because it doesn't specify which zeroes we want