Graphing a Basketball's Height Using Equations | Homework Help

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    Graphing
In summary, graphing is a visual representation of data using points, lines, bars, or other symbols to show the relationship between two or more variables. It is important because it allows for a quick and easy understanding of data, identifies patterns and trends, and allows for comparisons. There are different types of graphs, including line graphs, bar graphs, pie charts, scatter plots, and histograms, which should be chosen based on the type of data and the message to be conveyed. Some common mistakes to avoid when graphing data include using inappropriate scales, unclear labeling, and manipulating data for a false impression. Accuracy and unbiased representation of the data is crucial in graphing.
  • #1
Stripe
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Homework Statement


A basketball is thrown into the air, and it's height is determined by

h = 3/4t(20-t) where t = time.


Homework Equations


What is the greatest height the ball reaches


The Attempt at a Solution


Ok so i tried to graph this out but stuffed up, a bit hard to show here.

So first i expanded the rule into
h=15t-3/4t^2
or
h=-3/4t^2+15t
Now I'm just wondering how i would graph that?
 
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  • #2
you don't need to graph it, the maximum point occurs when dh/dt=0. So find the value of t for this height hmax
 
  • #3
Ahh i see thanks a lot :D
 
  • #4
Stripe said:

Homework Statement


A basketball is thrown into the air, and it's height is determined by

h = 3/4t(20-t) where t = time.


Homework Equations


What is the greatest height the ball reaches


The Attempt at a Solution


Ok so i tried to graph this out but stuffed up, a bit hard to show here.

So first i expanded the rule into
h=15t-3/4t^2
or
h=-3/4t^2+15t
Now I'm just wondering how i would graph that?
Since you posted this question in the Precalculus Math section, I assume that you haven't studied calculus just yet. The graph of the height function is a parabola that opens downward. You can find the vertex of the graph by completing the square, some exercises of which you did in another thread.

h = -3/4t2 + 15t
= -3/4(t2 - 20t)
= -3/4(t2 - 20t + 100) + 75
= -3/4(t - 10)2 + 75
 
  • #5
By the way, I started to reply that the graph was NOT a parabola but then realized I was interpreting what Stripe wrote incorrectly. I, and, I think, most people, would interpret "3/4t(20-t)" as 3/(4t(20-t)) which certainly is NOT a parabola and has no highest point.

Mark44 recognized that that could not correspond to a ball thrown upward and realized that Stripe meant y= (3/4)t(20-t).
 
  • #6
sorry about that it's hard trying to write equations on the computer lol
 
  • #7
= -3/4(t2 - 20t + 100) + 75
= -3/4(t - 10)2 + 75

So with that part where you completed the square, the + 75 is right because you do the opposide of -3/4 x 100?

Like i thought you were supposed to do the opposite of what's in the brackets, (-100) but I'm assuming because the -3/4 you instead do the opposite of -75?
 
  • #8
Stripe said:
= -3/4(t2 - 20t + 100) + 75
= -3/4(t - 10)2 + 75

So with that part where you completed the square, the + 75 is right because you do the opposide of -3/4 x 100?

Like i thought you were supposed to do the opposite of what's in the brackets, (-100) but I'm assuming because the -3/4 you instead do the opposite of -75?
In the first expression, the 100 inside the parentheses is really -75, so to keep the expression equal I had to counter that by adding 75. The net effect is that I added -75 + 75 to that expression, which makes it exactly equal to what I started with.
 
  • #9
Stripe said:
sorry about that it's hard trying to write equations on the computer lol

Stripe said:
= -3/4(t2 - 20t + 100) + 75
= -3/4(t - 10)2 + 75

So with that part where you completed the square, the + 75 is right because you do the opposide of -3/4 x 100?

Like i thought you were supposed to do the opposite of what's in the brackets, (-100) but I'm assuming because the -3/4 you instead do the opposite of -75?
Parentheses! (-3/4) or -(3/4) not "-3/4". And use "^" to indicate powers. (-3/4)*(t- 10)^2 is far clearer than "-3/4(t-10)2"!

Yes, it is "+ 75" because (-3/4)(t^2- 20t+ 100)+ 75= (-3/4)t^2+ 15t- 75+ 75= (-3/4)t^2+ 15t.
 

1. What is graphing?

Graphing is a visual representation of data using points, lines, bars, or other symbols to show the relationship between two or more variables.

2. Why is graphing important?

Graphing allows for a quick and easy understanding of data and can help identify patterns, trends, and outliers. It also allows for comparisons between different sets of data.

3. What are the different types of graphs?

There are several types of graphs, including line graphs, bar graphs, pie charts, scatter plots, and histograms. The type of graph used depends on the type of data being presented and the purpose of the graph.

4. How do I choose the best type of graph for my data?

The best type of graph for your data depends on the type of data you have and the message you want to convey. For example, if you want to show a trend over time, a line graph would be most appropriate, while a bar graph would be suitable for comparing different categories.

5. What are some common mistakes to avoid when graphing data?

Some common mistakes to avoid when graphing data include using inappropriate or misleading scales, not labeling axes clearly, and manipulating the data to create a false impression. It is important to accurately represent the data and present it in a clear and unbiased manner.

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