
Subject: graphing equations
If, for example, 4x^{2}12x+9=0 and 4x^{2}+12x9=0, which I'm assuming it does
since you can derive that equation from the first, why do those two
equations have different graphs?
Hi,
The two equations
1) 4x^{2}  12x + 9 = 0
and
2) 4x^{2} + 12x  9 = 0
are equivalent, as you suggest. You can easily get from 1) to 2) by multiplying both sides by 1. Since
4x^{2}  12x + 9 = (2x  3)^{2}
they are each equivalent to
(2x  3)^{2} = 0.
Hence the only x that satisfies 4x^{2}  12x + 9 = 0 is x = ^{3}/_{2}.
However, the functions
3) y = 4x^{2}  12x + 9
and
4) y = 4x^{2} + 12x  9
are different. If you multiply both sides of equation 3) by 1 you get
y = 4x^{2} + 12x  9
Which is not the sames as 4).
As I think you have observed the graph of equation 3) is a parabola that opens upward while the graph of equation 4) is a parabola that opens downward.
I hope this helps,
Penny
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