There's a line graph with 3 dolphins (it's the same dolphin at different spot of the jump) jumping out of the water and landing (they formed a parabola). The Y-axis represents Height in feet and the X-axis represents Time in Seconds. The points are (10,0), (13,5), (16,0).
A) The dolphin is 13 feet in the air after 5 seconds.
B) The dolphin jumped in the air at a distance of 10 feet and landed at a distance of 16 feet.
C) The dolphin is 5 feet in the air after 13 seconds.
D) The dolphin jumped in the air after 10 seconds and landed back in the water after 16 seconds.
23)
Part 1- Which of the following is the correct explanation of the x-intercepts?
I have D
Part 2- Which is the correct explanation of the vertex?
I have C
Part 3 - Determine the domain of the scenario.
I have all Real #s
Part 1 - Which of the following is the correct
#1 ok
#2 ok
#3 The only points we can use are those given. That would make the domain {10,13,16}.
But, they have said line is a parabola, so the function is continuous. The domain is thus [10,16].
I guess you could consider that they started counting at t=0, when the dolphins were under water, making the domain [0,16].
The wording is rather vague.
For the domain there are multiple answers.
a) 10<=X<=16
b) 0<=x<=13
c) 10<=x<=15
d) all real #s
I chose d
mistake with c, it suppose to be:
c) 10<=x<=13
C is not correct. The point (16,0) clearly indicates that 16 is in the domain. It has to be A.
explanation of the x-intercepts:
The x-intercepts of a graph represent the points where the graph intersects the x-axis. In this case, the x-intercepts are (10, 0) and (16, 0), meaning that the dolphin was at a height of 0 feet both at 10 seconds and 16 seconds. This corresponds to the moments when the dolphin jumps out of the water and when it lands back in the water, respectively.
Part 2 - Which is the correct explanation of the vertex:
The vertex of a parabolic graph, represented as (h, k), gives the coordinates of the highest or lowest point on the graph. In this case, the vertex can be found by examining the middle point of the parabola. The three points given are (10, 0), (13, 5), and (16, 0). The middle point, which is the highest point on the parabola, is (13, 5). This means that the dolphin reached a height of 5 feet at 13 seconds, making (13, 5) the vertex of the parabola.
Part 3 - Determine the domain of the scenario:
The domain of a scenario refers to the set of all possible input values, which, in this case, is the set of all possible time values. Since the dolphin's jump can be measured from the starting point (before it jumps) until it lands back in the water, the domain of this scenario would be all real numbers. Therefore, all possible time values are included in the domain.