The path of a softball is given by the equation y=0.08x^2 + x + 4.
The coordinates x and y are measured in feet, with x=0 corresponding to the position from which the ball was thrown.
A) Use a graphing utility to graph the trajectory of the softball.
B) Move the cursor along the path to approximate the highest point. Approximate the range of the trajectory.
there are many types of graphing calculators, it will be hard for somebody here to help you with the actual setting.
It is a disservice to students to "teach" this topic with a graphing calculator, it teaches you nothing about the quadratic function.
The question you pose is a standard simple question in that topic. I would solve it by completing the square or by doing the following:
the x of the vertex is -b/(2a)
=-1/.16 = 6.25
now sub that into the function and you have your maximum height.
I got 7.75 feet
the range would be 4 <= y <= 7.75
oops
looking back I had as the x of the vertex
as -1/16 which should have been -6.25
I will not proceed because the function you gave makes no sense for the trajectory of a thrown ball
It is a parabola which opens upwards, thus is has no maximum, but rather a minimum.
was the first term -.08x^2 ??
Based on the equation provided, the path of the softball is given by the equation y = 0.08x^2 + x + 4, where x and y are measured in feet and x = 0 corresponds to the position from which the ball was thrown.
A) To graph the trajectory of the softball using a graphing utility:
1. Open a graphing utility on your calculator or computer software.
2. Enter the equation y = 0.08x^2 + x + 4 into the graphing utility.
3. Set the appropriate x and y axes ranges to capture the desired portion of the graph.
4. Plot the graph to display the trajectory of the softball.
B) To approximate the highest point and determine the range of the trajectory:
1. Use the cursor or any navigation feature available in your graphing utility to move along the path of the softball.
2. Find the coordinates of the point where the softball reaches its highest point.
- This can be done by moving the cursor along the graph until the y-coordinate starts decreasing again, indicating the highest point.
- Record the x and y coordinates of this point.
3. The x-coordinate of the highest point represents the range of the trajectory.
- Approximate the x-coordinate value from the highest point as accurately as possible.
4. Calculate the corresponding y-coordinate of the highest point obtained from step 2 as the maximum height of the trajectory.
Please note that different graphing calculators may have slightly different procedures and interface, so you may need to consult the user manual or help documentation specific to your graphing calculator model for more specific instructions.