A ball is launched into the air and the height of the ball, in feet, is estimated \(\frac{1}{2}\) second after it is launched. The ball is then launched again and this time the height of the ball is estimated 1 second after it is launched. This experiment is repeated 16 times, and on the nth launch, the height of the ball is estimated \(\frac{n}{2}\) seconds after it is launched. The results are shown in the scatterplot below and a quadratic model that best fits the data is also shown.

Let \(a\) be the number of times the model predicts that the height of a launched ball will be exactly 8 feet and let b be the number of times the estimated height of the launched ball was 8 feet. What is the value of \(a+b \)?