Answer:
When the constant is positive:
It is the same quadratic function of f(x) = x² but it is shifted h units to the right.
When the constant is negative:
It is the same quadratic function of f(x) = x² but it is shifted h units to the left.
Step-by-step explanation:
We need to identify how is the graph of f(x) = x² is transformed when we change the function to f(x) = (x-h)² and h is a positive number.
So, if we have a function g(x) = f(x-h), we can say that g(x) is f(x) shifted h units to the right.
Therefore, when the constant is positive:
f(x) = (x-h)² is the same quadratic function of f(x) = x² but it is shifted h units to the right.
On the other hand, if we have a function g(x) = f(x+h), we can say that g(x) is f(x) shifted h units to the left.
Therefore, when the constant h is negative, we get that f(x) is equal to:
f(x) = (x - (-h))² = (x+h)²
So, f(x) = (x+h)² is the same quadratic function of f(x) = x² but it is shifted h units to the left.