A baseball is thrown directly upward with an initial velocity of 98 feet per second (or approximately 67 mph) from an initial height of 7 feet. The height of the ball (in feet) after t seconds is given by the formula: h(t) = -16t2 + 98t + 7 (If there was no air resistance, this equation would give accurate results. However, in reality, the air slows down the baseball and it would not actually go as high as you will calculate).
a. Draw a graph of the function by hand. Number the x-axis from 0 to 7 and the y-axis from 0 to 160. Make sure to keep a consistent scale and accurately label the x- and y-axes by what they represent in words. Use a ruler and graph paper to make a neat graph.
b.
c.
Find the vertex. Show all work.
What is the maximum height of the ball? How is this represented on the graph?
d.
on the graph?
After how many seconds will the ball reach its maximum height? How is this represented
e. After how many seconds will the ball hit the ground? Show all work, and express your solution as an exact simplified radical and as a decimal approximation to the nearest 0.01 seconds. How is this represented on the graph?