Answers:
- Choice B
- Choice D
- Choice E
- Choice G
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Explanation:
Let's go through the answer choices to see which are true or which are false.
- A) False. The x intercepts, not the y intercept, tell us when the ball hits the ground. This is because the ball hits the ground whenever y = 0.
- B) True. The vertical intercept, aka y intercept, happens when x = 0. The ball is dropped at x = 0 which is the starting time value.
- C) False. The max height of the ball occurs when x = 0, as shown by the highest peak. Afterward, the ball bounces and decreases height gradually.
- D) True. The max height is y = 2 and this is the y intercept where the curve crosses the y axis.
- E) True. The x intercepts indicate when the ball hits the ground. The first time somewhere between 0.6 and 0.8 seconds. The second time at or around 1.6 seconds. The third time being at or around 2.2 seconds. The gap between x intercepts shrinks as time goes on to indicate that the ball bounces slowly at first, but those bounces speed up (and the height of each bounce decreases).
- F) False. The function has the minimum values at each moment it hits the ground, so whenever y = 0 is a minimum point. Simply look for the lowest point. If the graph went down forever to negative infinity, then we could say that there are no absolute minimum values.
- G) True. Each min point occurs when y = 0, which are the lowest points.
