SOLUTION: The height in feet, h, reached by a softball after t seconds is given by the function h(t) = −16t2 + 87t + 3. During what time interval did the softball reach an altitude

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The height in feet, h, reached by a softball after t seconds is given by the function h(t) = −16t2 + 87t + 3. During what time interval did the softball reach an altitude      Log On


   

Question 1098932: The height in feet, h, reached by a softball after t seconds is given by the function
h(t) = −16t2 + 87t + 3.
During what time interval did the softball reach an altitude of at least 80 ft? Round to 2 decimal places. (Enter your answer using interval notation.)
The answer I came up with was [.18,5.26]
My teacher looked and doesn't know why the computer counted this wrong.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I'll try it:
+h%28t%29+=+-16t%5E2+%2B+87t+%2B+3+
+80+=+-16t%5E2+%2B+87t+%2B+3+
+-16t%5E2+%2B+87t+-+77+=+0+
Use quadratic formula
+t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+-16+
+b+=+87+
+c+=+-77+
+t+=+%28+-87+%2B-+sqrt%28+87%5E2-4%2A%28-16%29%2A%28-77%29+%29%29%2F%282%2A%28-16%29%29+
+t+=+%28+-87+%2B-+sqrt%28+7569+-+4928+%29+%29+%2F+%28+-32+%29+
+t+=+%28+-87+%2B-+sqrt%28+2641+%29+%29+%2F+%28+-32+%29+
+t+=+%28+-87+%2B+51.39067+%29+%2F+%28-32+%29+
+t+=+-35.60934+%2F+%28-32%29+
+t+=+1.1128+
and
+t+=+%28+-87+-+51.39067+%29+%2F+%28-32%29+
+t+=+-138.39067+%2F+%28+-32+%29+
+t+=+4.3247+
The softball reaches at least a height of 80 ft
between 1.11 sec and 4.32 sec
------------------------------------------
check:
Here's the plot of h(t):
+graph%28+400%2C400%2C+-1%2C+8%2C+-10%2C+130%2C+-16x%5E2+%2B+87x+%2B+3+%29+
My answers look at least close