Math Component

A cannonball is shot upward from the upper deck of a fort with an initial velocity of 192 feet per second.  The deck is 32 feet above the ground. How high does the cannonball go? How long is the cannonball in the air?

-- Quadratic Model: -16x²+192x+32

To answer the first question, it can easily be graphed and calculated to be fast, which is what I did for accuracy, but the vertex can be calculated using the quadratic formula. The value –b/2a is the x value of the vertex, and it can be plugged into the model to get the y value. In this case the vertex is (6, 508) which states that the highest point the cannon ball got to was 508 feet in the air.

The second question can also be easily solved with a calculator, which is exactly what I did. I entered the quadratic model into the calculator, clicked second, then trace and used the find zeros function, which gave me 12.1 as the positive zero. Now this may seem like an error on my part since the x value in the vertex is also the location of the axis of symmetry, and there must be equal distance between the center and the zeros on both sides. However, the existence of the c value in this quadratic model makes the first root move into the negative. To answer the question, the cannon ball was in the air for 12.1 seconds.