Question

Write a formula for the function obtained from the graph has shifted as described.f(x)=x^2 is shifted up 1 unit and to the left 2 units.The new equations f(x)= ?

Answer 1

The new equation is f(x) = (x+2)² + 1

Step-by-step explanation

• If f(x) shifts up m units, then the new formula of the function = f(x) + m

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• If f(x) shift down n units, then the new formula of the function = f(x) - n

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• If f(x) shifts right P - units, then the new formula of the function = f(x-p)

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• If f(x) shifts left q units, then the new formula of the function = f(x+q)

From the given function, first, f(x) = x² is shifted up 1 unit

⇒ f(x) = x² + 1

Then, shifted to the left 2 units.

⇒ f(x) = (x+2)² + 1

Hence, the new equation is f(x) = (x+2)² + 1