Start with x2=6x-1. I can create two two quadratic equations in standard form from this starting point: x2-6x+1=0 and -x2+6x-1=0. If I plot parabolas for these two equations, one opens up and one opens down (they both have the same x-intercepts). Which one of the two should I use? (I realize that I am dealing with specific points here and not a general function, so maybe plotted parabolas are really not appropriate.) Any insight into this situation would be appreciated. Thanks.
Question about manipulation of quadratic equations: Start with x^2=6x-1...
- Thread starter dmurley
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- Apr 12, 2005
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You have not understood what you have said.
1) x^2 - 6x + 1 = 0 is an equation that can be solved. It is NOT a function to be graphed.
2) -x^2 + 6x - 1 = 0 is an equivalent equation that can be solved.
You should find that 1) and 2) have the same solutions. You should also find in your readings that 2) is NOT in "Standard Form".
y = x^2 - 6x + 1 or f(x) = x^2 - 6x + 1 are function definitions or relations that can be graphed on an x-,y-coordinate system.
y = -x^2 + 6x - 1 or g(x) = -x^2 + 6x - 1 are related function definitions or relations that can be graphed on an x-,y-coordinate system.
You should find these properties:
f(x) and g(x) are reflections of each other across the x-axis.
f(x) and g(x) have the same zeros.
No need to be confused if you have good definitions.
1) x^2 - 6x + 1 = 0 is an equation that can be solved. It is NOT a function to be graphed.
2) -x^2 + 6x - 1 = 0 is an equivalent equation that can be solved.
You should find that 1) and 2) have the same solutions. You should also find in your readings that 2) is NOT in "Standard Form".
y = x^2 - 6x + 1 or f(x) = x^2 - 6x + 1 are function definitions or relations that can be graphed on an x-,y-coordinate system.
y = -x^2 + 6x - 1 or g(x) = -x^2 + 6x - 1 are related function definitions or relations that can be graphed on an x-,y-coordinate system.
You should find these properties:
f(x) and g(x) are reflections of each other across the x-axis.
f(x) and g(x) have the same zeros.
No need to be confused if you have good definitions.