Question

The graph of Fx), shown below, has

the same shape as the graph of
G(X)=x2 but is shifted right by 3 units
and down by 2 units. Write the
equation for F(x)

Answer 1

f(x) = (x - 3)²- 2

Explanation:

Given the graph of f(x), where it has the same shape as the graph of g(x) = x², but is shifted right by 3 units, and down by 2 units.

The horizontal translation of the parent graph parabola, g(x) = x², is represented by y = (x - h)², where the graph shifts by h units to the right, such that h > 0.

The vertical translation of the parent graph is represented by y = f(x - h)² - k, where the graph is vertically translated by |k | units downward, such that k < 0.

Therefore, the equation that represents the vertical and horizontal translations of the graph is: f(x) = (x - 3)²- 2.