QUIZ 1 SOLUTIONS
An unthinking person in a hot air balloon throws an object up into the air. The height H(t) (in feet) of the object, as a function of time t (in seconds), is given by the formula H(t) =
1. Using the axes below, graph H as a function of t, clearly indicating and giving the coordinates of all intercepts.
To find the H-intercept, set t = 0: H = , so the H-intercept is the point (0,96).
To find the t-intercepts, set H = 0: 0 = = . So t = or t = 3 and the t-intercepts are (-2,0) and (3,0).
The function is quadratic so its graph will be a parabola, opening downward since the coefficient of is negative. The vertex is found by t = = = 1/2. Find the H-coordinate of the vertex by setting t = 1/2: H = = = 100.
2. At what time will the object reach its maximum height?
From the vertex we see the answer is t = 1/2 sec.
3. What is the maximum height?
From the vertex we see the answer is H = 100 ft.