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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
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 Originally Posted by Luke 2087 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. Tags questions Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post vickyc95 Number Theory 4 May 24th, 2016 07:20 PM Valar30 Calculus 17 January 4th, 2011 07:58 PM RMG46 Algebra 17 June 20th, 2010 09:31 PM tobymac Algebra 2 June 12th, 2009 09:33 AM blackobisk Algebra 1 January 27th, 2009 11:15 AM

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