SOLUTION: Write an equation for the horizontal translation of f(x)=xsquared 3.7 units right We have no idea where to start to answer this question.

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Question 901413: Write an equation for the horizontal translation of f(x)=xsquared
3.7 units right
We have no idea where to start to answer this question.
Found 2 solutions by rothauserc, MathLover1:
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
we are given f(x) = x^2
we want a horizontal translation of 3.7 units to the right, the rule for shifting f(x) left or right is:
f(x + b) gives f(x) shifted b units to the left. Shifting to the right works the same way; f(x – b) is f(x) shifted b units to the right.
now we can write the solution
f(x-3.7) = (x-3.7)^2
lets look at the graphs, red line is f(x) = x^2, green line is f(x-3.7) = (x-3.7)^2
+graph%28+300%2C+200%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%2C+%28x-3.7%29%5E2%29+

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
The transformations rules can be summarized as:
f%28x%29+%2B+a- means f%28x%29 shifted upward a+units+
f%28x%29+-a- means f%28x%29 shifted downward a units+
f%28x+%2B+a%29- means f%28x%29 shifted left a units+
highlight%28f%28x+-a%29%29- means f%28x%29 shifted right a units+
-f%28x%29- means f%28x%29 is flipped upside+down (reflected about the x-axis)
f%28-x%29 is the mirror of f%28x%29 (reflected about the y-axis)
you are given f%28x%29=x%5E2
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C++x%5E2%29+

and you need to find an equation for the horizontal translation of
f%28x%29=x%5E2 3.7 units right, you need f%28x-a%29+
f%28x-a%29=%28x-a%29%5E2+ where a=3.7
f%28x-3.7%29=%28x-3.7%29%5E2
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C++%28x-3.7%29%5E2%29+

let's see both functions on same graph:

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C++x%5E2%2C%28x-3.7%29%5E2%29+