SOLUTION: A rectangle has an area given by A=-6w^2+72w . What is the maximum area for this rectangle? (Hint: Where does the maximum value occur?)

Algebra ->  Surface-area -> SOLUTION: A rectangle has an area given by A=-6w^2+72w . What is the maximum area for this rectangle? (Hint: Where does the maximum value occur?)      Log On


   

Question 322121: A rectangle has an area given by A=-6w^2+72w . What is the maximum area for this rectangle? (Hint: Where does the maximum value occur?)
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
review explaination below
w=-0,12
-6%2812%29%5E2%2B72%2812%29
-6%28144%29%2B864
-864%2B864
0
A=-6w%5E2%2B72w thruogh guess and check doing the quadratic formula several times with different amouts i came to find the following:
if A=217 then it is an imaginary answer so A has to equal 216 as its maximum
216=-6w^2+72w
0=-6w^2+72w-216
W=6
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aw%5E2%2Bbw%2Bc=0 (in our case -6w%5E2%2B72w%2B0+=+0) has the following solutons:

w%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2872%29%5E2-4%2A-6%2A0=5184.

Discriminant d=5184 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-72%2B-sqrt%28+5184+%29%29%2F2%5Ca.

w%5B1%5D+=+%28-%2872%29%2Bsqrt%28+5184+%29%29%2F2%5C-6+=+0
w%5B2%5D+=+%28-%2872%29-sqrt%28+5184+%29%29%2F2%5C-6+=+12

Quadratic expression -6w%5E2%2B72w%2B0 can be factored:
-6w%5E2%2B72w%2B0+=+-6%28w-0%29%2A%28w-12%29
Again, the answer is: 0, 12. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-6%2Ax%5E2%2B72%2Ax%2B0+%29