SOLUTION: Neglecting air resistance, the height of a projectile fired vertically into the air at an initial velocity of 112 feet per second is a function of time x and is given by the equati

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Neglecting air resistance, the height of a projectile fired vertically into the air at an initial velocity of 112 feet per second is a function of time x and is given by the equati      Log On


   

Question 764742: Neglecting air resistance, the height of a projectile fired vertically into the air at an initial velocity of 112 feet per second is a function of time x and is given by the equation f(x) = 112x - 16x2. Find the highest point reached by the projectile.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+f%28x%29+=+112x+-+16x%5E2+
This is a parabola in the form
+f%28x%29+=+ax%5E2+%2B+b%2Ax+
The x-coordinate of the
vertex ( maximum height )
is at +-b+%2F+%282a%29+
----------------
+a+=+-16+
+b+=+112+
------------
+-b%2F%282a%29+=+-112+%2F+%28+2%2A%28-16%29%29+
+-b%2F%282a%29+=+3.5+
Now find +f%283.5%29+
+f%283.5%29+=+112%2A3.5+-+16%2A3.5%5E2+
+f%283.5%29+=+392+-+196+
+f%283.5%29+=+196+
The highest point is at 196 ft
Here's the plot:
+graph%28+400%2C+400%2C+-2%2C+12%2C+-20%2C+220%2C+-16x%5E2+%2B+112x+%29+