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# Graph interpretation word problem: basketball

CCSS.Math:

## Video transcript

mr. Theisen is honing his deadly three-point precision on the basketball court for one of his shots the height of the ball in feet as a function of horizontal distance as a function of horizontal distance and feet Y of X so here Y is a function of X so the height must be Y because that's the thing that is a function of something else so this right over here is height so our y-axis is going to represent height and it is a function of X so X must represent horizontal distance because height is a function of horizontal distance so this right over here is horizontal horizontal distance so this is horizontal distance now it's plotted below mr. Theisen is standing at x equals 0 so he's standing right over here this is mr. Theisen so draw my best attempt to draw a little stick figure version of mr. Theisen that's not even an acceptable stick figure right over there so this is this is mr. Theisen and he's standing at x equals 0 and at x equals 0 he is shooting a basketball he is shooting a basketball and you see from the function right over here that where the heck were the where the graph intersects the y axis that tells us that's that's essentially the height of the ball when x is equal 0 where its where mr. Theisen is standing and if we look at this this looks like it's 2 4 6 feet 6 feet high so that's really the initial position of the ball when mr. Theisen is about to let go of it then he lets go of it and the ball goes in this parabolic trajectory it increases increases increasing increases it looks like it hits a maximum point right around right around there roughly that looks like it's at about 16 feet and then it starts to go down and right over here and this looks like it's about let's see 22 24 26 feet out it looks like it hits something and considering that something is 10 feet high it's reasonable to assume that thing that it hits is the goal and especially because he says that he has or the the question states that he has deadly three-point precision we can assume it's not crazy that he actually makes the goal and so that's where it goes into the net and then the net forces the ball to go down at a much deeper at a much deeper trajectory and this is exactly of course ten feet high the height of the goal now let's see which of these interpretations are consistent with the interpretation that we just did the ball is released from mr. Thiessen's hand at a height of 6 feet well that looks exactly right when X is equal to 0 the ball is 6 feet and not only is that right but that is considers the significance of the y-intercept of this function the y-intercept is the value of y the height when x is equal to 0 so that is indeed the Y that is the significance of the y-intercept look it let's look at these other things mr. Theisen is shooting the basketball from 26 feet away well that's right he's at x equals 0 the goal is at 26 feet away but that's not the significance of that's not the significance of the y-intercept that be the significance of where we saw this little point here that started to where the ball dropped down at a more at a steeper angle the rim of the basketball hoop is 10 feet high once again that's true you can look at it you can see it right over there but that's not the significance of the y-intercept the maximum height the ball reaches is 16 feet well once again that is true but that's the significance of this maximum point on the curve that's not the significance of the y-intercept so we'll go with this first choice