Question

Function g can be thought of as a translated (shifted) version of f(x)=x^2 Write the equation for g(x),

Answer 1

g(x) = (x - a)² or

g(x) = (x + a)² or

g(x) = x² + a or

g(x) = (x + b)² + a or

g(x) = (x + b)² - a or

g(x) = (x - b)² + a or

g(x) = (x - b)² - a

Explanation:

Given equation:

f(x) = x²

This is the equation of a parabola with turning points at (0,0) facing up.

Now;

g(x) which is a shifted version of f(x) will have one of many forms depending on the nature of translation.

If f(x) = x² is shifted to the right by a units, then;

g(x) = (x - a)²

If f(x) = x² is shifted to the left by a units, then;

g(x) = (x + a)²

If f(x) = x² is shifted upwards by a units, then;

g(x) = x² + a

If f(x) = x² is shifted downwards by a units, then;

g(x) = x² - a

If f(x) = x² is shifted upwards by a units and to the left by b units, then;

g(x) = (x + b)² + a

If f(x) = x² is shifted downwards by a units and to the left by b units, then;

g(x) = (x + b)² - a

If f(x) = x² is shifted upwards by a units and to the right by b units, then;

g(x) = (x - b)² + a

If f(x) = x² is shifted downwards by a units and to the right by b units, then;

g(x) = (x - b)² - a