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二次函数（续）
我们能从二次函数的变化中观察到哪些规律？
1. Modeling falling objects
Modeling falling objects
2. How quadratic functions change
How quadratic functions change
3. Summary
Summary
4. Building the height model
A balloon leaves a window 37 feet up with an initial upward velocity of 41 feet per second. Which model gives its height s at time t?
5. Landing time estimate from the graph
Reading the graph of s(t) = -16t^2 + 41t + 37, at what time does the balloon appear to land? Give seconds to one decimal place.
6. Exact landing time
Solving -16t^2 + 41t + 37 = 0 exactly, what is the positive landing time? Round to two decimal places.
7. Time to the highest point
For s(t) = -16t^2 + 41t + 37, at what time does the balloon reach its highest point? Round to two decimal places.
8. Falling average rates
On the descending part of the balloon's flight the average rates on [1.5,2], [2,2.5], [2.5,3] are -15, -31 and -47 ft/s. What do these values show?
9. Reading formulas from two graphs
Two parabolas are given only by their graphs, each showing the vertex and one more labeled point. What is the right strategy to recover their formulas?
10. Vertex form of a basic parabola
For f(x) = (1/2)(x - 2)^2 + 1, what is the minimum value of f?
11. Symmetric height of the balloon
A balloon launched from 56.3 feet reaches its highest point at t = 1.2 seconds. What is its height at t = 2.4 seconds, in feet?
12. A downward parabola can have no x-intercepts
A parabola with a negative leading coefficient must cross the x-axis twice.