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Question 446237: In the equation of a parabola y = (x-5)^2 + 4, I understand the vertex is (5,4). I don't understand why we take the opposite of what is in the parenthesis with the x. It seems to me we would translate the vertex of the graph left 5 units, not right 5 units. Can someone please help me understand this? Thanks.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In the equation of a parabola y = (x-5)^2 + 4, I understand the vertex is (5,4). I don't understand why we take the opposite of what is in the parenthesis with the x. It seems to me we would translate the vertex of the graph left 5 units, not right 5 units.
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Try thinking of it this way.
If you had the equation y = x^2+4
y would be 4 when x is zero.
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You have the equation y = (x-5)^2 + 4
y will be 4 when (x-5) is zero.
That happens when x = 5.
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What happened before at x = 0 now
happens when x = 5.
The graph has moved 5 to the right.
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This is the way I teach the idea.
Think of the x-axis as a time line where
time flows from left to right i.e. 0 seconds, 1 second, ...., 5 seconds etc.
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t is some time on the t-axis.
t-5 is 5 seconds later on the t-axis.
"later" means to the right.
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t+5 would mean 5 seconds earlier.
"earlier" means to the left.
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Hope this helps.
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Cheers,
Stan H.
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