SOLUTION: Looking at {{{f(x)=-0.2x^2+12x+11}}} Use the quadratic equation to determine the last day that tickets will be sold. (Note: Write your answer in terms of the number of days af

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Looking at {{{f(x)=-0.2x^2+12x+11}}} Use the quadratic equation to determine the last day that tickets will be sold. (Note: Write your answer in terms of the number of days af      Log On


   

Question 130296: Looking at f%28x%29=-0.2x%5E2%2B12x%2B11

Use the quadratic equation to determine the last day that tickets will be sold. (Note: Write your answer in terms of the number of days after ticket sales begin.)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The last day of ticket sales will correspond to the rightmost zero. So we need to find the zeros



y=-0.2x%5E2%2B12x%2B11 Start with the given equation


0=-0.2x%5E2%2B12x%2B11 Set y equal to zero


10%280%29=10%28-0.2x%5E2%2B12x%2B11%29 Multiply both sides by 10 to get rid of the decimal number


0=-2x%5E2%2B120x%2B110 Distribute and multiply


Let's use the quadratic formula to solve for x:


Starting with the general quadratic

ax%5E2%2Bbx%2Bc=0

the general solution using the quadratic equation is:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29



So lets solve -2%2Ax%5E2%2B120%2Ax%2B110=0 ( notice a=-2, b=120, and c=110)




x+=+%28-120+%2B-+sqrt%28+%28120%29%5E2-4%2A-2%2A110+%29%29%2F%282%2A-2%29 Plug in a=-2, b=120, and c=110



x+=+%28-120+%2B-+sqrt%28+14400-4%2A-2%2A110+%29%29%2F%282%2A-2%29 Square 120 to get 14400



x+=+%28-120+%2B-+sqrt%28+14400%2B880+%29%29%2F%282%2A-2%29 Multiply -4%2A110%2A-2 to get 880



x+=+%28-120+%2B-+sqrt%28+15280+%29%29%2F%282%2A-2%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-120+%2B-+4%2Asqrt%28955%29%29%2F%282%2A-2%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%28-120+%2B-+4%2Asqrt%28955%29%29%2F-4 Multiply 2 and -2 to get -4

So now the expression breaks down into two parts

x+=+%28-120+%2B+4%2Asqrt%28955%29%29%2F-4 or x+=+%28-120+-+4%2Asqrt%28955%29%29%2F-4


Now break up the fraction


x=-120%2F-4%2B4%2Asqrt%28955%29%2F-4 or x=-120%2F-4-4%2Asqrt%28955%29%2F-4


Simplify


x=30-sqrt%28955%29 or x=30%2Bsqrt%28955%29


So these expressions approximate to

x=-0.903074280724887 or x=60.9030742807249


So our solutions are:
x=-0.903074280724887 or x=60.9030742807249



So the last day of ticket sales will be on the 60th day