SOLUTION: Suppose the function h=-16t^2+38t models the height h in feet of a ball at a time t in seconds. Can the ball reach 25 feet? 20ft? What is the max height of the ball and how long wi

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Suppose the function h=-16t^2+38t models the height h in feet of a ball at a time t in seconds. Can the ball reach 25 feet? 20ft? What is the max height of the ball and how long wi      Log On


   

Question 915633: Suppose the function h=-16t^2+38t models the height h in feet of a ball at a time t in seconds. Can the ball reach 25 feet? 20ft? What is the max height of the ball and how long will it take to get there? Please show work!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
When the equation has the form
+a%2Ax%5E2+%2B+b%2Ax+%2B+c+, then the
x-coordinate of the maximum is
at +-b%2F%282a%29+
------------------
In this equation:
+h+=+-16t%5E2+%2B+38t+
+-b%2F%282a%29+=+-38%2F%282%2A%28-16%29%29+
+-b%2F%282a%29+=+19%2F16+
This is the value of +t%5Bmax%5D+
in seconds
+t%5Bmax%5D+=+1.188+ sec
-----------------
+h%5Bmax%5D+=+-16%2A%2819%2F16%29%5E2+%2B+38%2A%2819%2F16%29+
+h%5Bmax%5D+=+-361%2F16+%2B+722%2F16+
+h%5Bmax%5D+=+361%2F16+
+h%5Bmax%5D+=+22.563+ ft
-----------------
The ball reaches 20 ft, but not 25 ft
Here's the plot:
+graph%28+400%2C+400%2C+-1%2C+3%2C+-2%2C+25%2C+-16x%5E2+%2B+38x+%29+