We want to find how long the ball is in the air. To do so, we need to solve the equation below.
- 16t^2 +47t+3=0
We will use a graphing calculator to solve it. We first draw the related function f(x)=- 16x^2 +47x+3, and then use the zero option in the calculator.
[- 2, 6] scl: 1 by [- 15, 45] scl:5
The positive x-intercept of the graph is 3. Therefore, the ball is in the air for 3 seconds.
Showing Our Work
Drawing Related Function
We want to draw the related function.
f(x)=- 16x^2 +47x+3
We will enter it in the calculator by pushing Y= and writing it in the first row.
Next, by pushing GRAPH, the calculator will draw the graph of the equation. For this function to be visible on the screen, we have to resize the standard window by pushing the WINDOW button. We will change the settings to a more appropriate size and then push GRAPH.
Now we are able to see that the graph intersects the x-axis twice and there are two zeros. To find them, we can use the zero option in the calculator. This can be found by pressing 2ND and then CALC.
After selecting the "zero" option, we need to choose left and right boundaries for one of the zeros. Finally, the calculator asks for a guess where the zero might be. After that, it will calculate the exact point for us. We will have to do this twice, once for each zero.
