My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Thanks Tree2Thanks
  • 2 Post By v8archie
Reply
 
LinkBack Thread Tools Display Modes
June 21st, 2017, 06:56 PM   #1
Newbie
 
Joined: Apr 2017
From: Canada

Posts: 24
Thanks: 1

Parabola Strange Question

The following relationship gives the height, "h" in meters, of a soccer ball, as a function of the horizontal distance, d meters, the ball travels until it first hits the ground:

h = -0.025(d-20)^2 + 10

Q: If the origin were placed at the vertex of the parabola, what would be the equation of the curve?

I have given this some thought and figured that (h,k) of the vertex would double to make (2h,2k) since both the horizontal and vertical distances are increasing by 20 and 10.

This would make my new equation:

h = -0.025(d-40)^2 + 20

The answer provided is different. Apparently, the new curve would be:

h =-0.025(d^2)

Could you help me understand?
Antoniomathgini is offline  
 
June 21st, 2017, 08:05 PM   #2
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 6,936
Thanks: 2265

Math Focus: Mainly analysis and algebra
1) Where is the vertex? $(d,h)=(20,10)$ can you see why?
2) If we translate the plane so that the $(d,h)=(20,10)$ becomes the origin, $(D,H)=(0,0)$, we are saying that $D=d-20$ and $H=h-10$.
3) The equation $h = -0.025(d-20)^2 + 10$ can then be transformed as follows:
\begin{align*}
h &= -0.025(d-20)^2 + 10 \\
h-10 &= -0.025(d-20)^2 \\
H &= -0.025D^2
\end{align*}
Thanks from topsquark and Antoniomathgini
v8archie is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
parabola, question, strange



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Strange differentiation question tankertert Calculus 10 April 30th, 2012 01:15 PM
Strange Integral Question (possbily parametric) master555 Real Analysis 3 January 23rd, 2012 11:48 PM
Riemann Summ Limit Proof (strange question to me) master555 Real Analysis 1 January 14th, 2012 11:55 AM
parabola question? khyratmath123 Calculus 1 December 15th, 2010 05:45 AM
Parabola Question julian21 Algebra 3 November 17th, 2010 08:07 AM





Copyright © 2017 My Math Forum. All rights reserved.