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What is the transformation of f(x) = x^2 When the constant is positive When the constant is negative

What is the transformation of f(x) = x^2 When the constant is positive When the constant-example-1

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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.

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