I've noticed many questions I'm assigned about quadratics are asking to 'relate formulas to f(x)=x^2'. Depending on the given formula (ex. f(x)=(x-5)^2) the graph might move right, left, up, or down and that's what they're trying to ask for. Can someone explain, mathematically, how this relativity works? Even taking the example above, why does the graph look the same as that of y=x^2 but is moved to the right, even though there is a drastic difference between having x^2 and (x-5)^2?
Quadratic formulas and their relativity
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BigBeachBanana
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Steven G
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why does the graph look the same as that of y=x^2 but is moved to the right, even though there is a drastic difference between having x^2 and (x-5)^2?
I do not agree that that there is a drastic difference between x^2 and (x-5)^2
Just make a x-y table for both graph. Pick x= 1, 2, 3, 4 and 5 for y=x^2 and x= 6, 7, 8, 9 and 10 for y=(x-5)^2. Note that for the x's for y=(x-5)^2 I made them 5 more than the x's for y=x^2. What do you notice for the y values in both tables? Why did I make the x-values 5 more for y=(x-5)^2?
I do not agree that that there is a drastic difference between x^2 and (x-5)^2
Just make a x-y table for both graph. Pick x= 1, 2, 3, 4 and 5 for y=x^2 and x= 6, 7, 8, 9 and 10 for y=(x-5)^2. Note that for the x's for y=(x-5)^2 I made them 5 more than the x's for y=x^2. What do you notice for the y values in both tables? Why did I make the x-values 5 more for y=(x-5)^2?