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November 8th, 2017, 05:29 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. 
November 8th, 2017, 02:36 PM  #2  
Senior Member Joined: Sep 2015 From: USA Posts: 2,428 Thanks: 1314  Quote:
$(x, f(x))$ 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.  

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