SOLUTION: 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

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.
-----------------
Try thinking of it this way.
If you had the equation y = x^2+4
y would be 4 when x is zero.
---------------------------------------
You have the equation y = (x-5)^2 + 4
y will be 4 when (x-5) is zero.
That happens when x = 5.
-------------------------------------
What happened before at x = 0 now
happens when x = 5.
The graph has moved 5 to the right.
-------------------------------------------
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.
---
t is some time on the t-axis.
t-5 is 5 seconds later on the t-axis.
"later" means to the right.
---
t+5 would mean 5 seconds earlier.
"earlier" means to the left.
===============================
Hope this helps.
===================
Cheers,
Stan H.
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