Graphing a Basketball's Height Using Equations | Homework Help

[Stripe]

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?

 

[rock.freak667]

you don't need to graph it, the maximum point occurs when dh/dt=0. So find the value of t for this height h_max

 

[Stripe]

Ahh i see thanks a lot :D

 

[Mark44]

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

 

[HallsofIvy]

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).

 

[Stripe]

sorry about that it's hard trying to write equations on the computer lol

 

[Stripe]

= -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?

 

[Mark44]

= -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.

 

[HallsofIvy]

sorry about that it's hard trying to write equations on the computer lol

= -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.