My Math Forum  

Go Back   My Math Forum > College Math Forum > Linear Algebra

Linear Algebra Linear Algebra Math Forum


Thanks Tree1Thanks
  • 1 Post By romsek
Reply
 
LinkBack Thread Tools Display Modes
November 8th, 2017, 06:29 AM   #1
Newbie
 
Joined: Nov 2017
From: Brazil

Posts: 1
Thanks: 0

Need help with some questions

Hi ppl. Please I need some help with these questions.


Considering the parable with the function f(x) = -x² + 4x - 3.

How do I prove that the point (2,1) belongs to the parable?

And, also:

Given the linear transformation T: R2 -> R2 : T1 (x,y) = ( cosθ * x - senθ * y , senθ * x + cosθ * y

Given the angle θ = 150º, determine the rotation and the root positions of the parable after the linear transformation

Thanks in advance in any help that could be provided.
Luke 2087 is offline  
 
November 8th, 2017, 03:36 PM   #2
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: USA

Posts: 1,652
Thanks: 838

Quote:
Originally Posted by Luke 2087 View Post
Hi ppl. Please I need some help with these questions.


Considering the parable with the function f(x) = -x² + 4x - 3.

How do I prove that the point (2,1) belongs to the parable?

And, also:

Given the linear transformation T: R2 -> R2 : T1 (x,y) = ( cosθ * x - senθ * y , senθ * x + cosθ * y

Given the angle θ = 150º, determine the rotation and the root positions of the parable after the linear transformation

Thanks in advance in any help that could be provided.
a point that lies on a curve given by a function $f(x)$ will be of the form

$(x, f(x))$

so let's take a look

$f(2) = -(2)^2 + 4(2) - 3 = -4 + 8 - 3 = 1$

so yes, the point $(2,1)$ lies on the parabola given by $f(x)$

for the 2nd bit first you have to find the roots. There will be 2 of them, call them $r_1,~r_2$

the points will then be $(r_1, 0), ~(r_2, 0)$

and just apply T to those 2 points.
Thanks from topsquark
romsek is online now  
Reply

  My Math Forum > College Math Forum > Linear Algebra

Tags
questions



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Can anyone help me solve these questions? modulo questions vickyc95 Number Theory 4 May 24th, 2016 08:20 PM
2 questions. Valar30 Calculus 17 January 4th, 2011 08:58 PM
Some Questions RMG46 Algebra 17 June 20th, 2010 10:31 PM
A few questions for ya tobymac Algebra 2 June 12th, 2009 10:33 AM
Help on some questions blackobisk Algebra 1 January 27th, 2009 12:15 PM





Copyright © 2017 My Math Forum. All rights reserved.