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 February 21st, 2016, 11:09 PM #1 Newbie   Joined: Feb 2016 From: Shoeburyness, England Posts: 1 Thanks: 0 Quadratic equations and negative values of x^2 Hi, I'm completely new to this forum so please bear with me if this question has been asked before. I've been going back to basics and reinforcing a lot of my maths knowledge and my current topic is quadratic equations and sketching graphs. I've got no problems with this at all - my question is more of a conceptual issue. Take the example x^2 - 2x -3 = 0 Bog standard quadratic with a U shaped graph with solutions for x = -1 and 3 and the largest value of y coords = (1,-4). No probs. If I then reverse the signs on that equation: -x^2 +2x +3 = 0 Again in terms of the math I totally get that the x solutions remain unchanged and producing values for y coords produces (1,4) The problem I'm having is that conceptually to me the two equations are the same - I've just rearranged the signs, so x^2 -2x -3 = -x^2 +2x +3 = 0 So if they are they same, why does changing the signs produce a mirrored image of the quadratic curve about the x axis? Is there a mathematical explanation for this? Am I right to say that the two equations are equal when they produce different graphs? I hope my question makes sense and I look forward to hearing from the forum. Regards Mark
 February 21st, 2016, 11:37 PM #2 Senior Member   Joined: Dec 2015 From: holland Posts: 162 Thanks: 37 Math Focus: tetration x^2 - 2x - 3 = 0 true -x^2 + 2x + 3 = 0 true x^2 - 2x -3 = -x^2 + 2x + 3 is a false generalisation
February 22nd, 2016, 12:00 AM   #3
Senior Member

Joined: Dec 2015
From: holland

Posts: 162
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Math Focus: tetration
Quote:
 Originally Posted by manus x^2 - 2x - 3 = 0 true -x^2 + 2x + 3 = 0 true x^2 - 2x -3 = -x^2 + 2x + 3 is a false generalisation
x^2 - 2x - 3 = -x^2 + 2x + 3 is only true for the zeroes of the polynomial i.e x= -1 or x = 3

 February 22nd, 2016, 09:33 AM #4 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 Yes, the graph of $\displaystyle y= x^2- 2x- 3= (x- 3)(x+ 1)$ is a parabola, opening upward, with vertex at (1, -4). The graph of $\displaystyle y= -(x^2- 2x- 3)= -x^2+ 2x+ 3$ is a parabola, opening downward ,with vertex at (1, 4). Both of them cross the x-axis at (-1, 0) and (3, 0). There can be many different parabola that cross the x-axis at exactly the same place! Thanks from manus

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