The graph of fin blue is translated a whole number of units

The graph of f(in blue) is translated a whole number of units horizontally and vertically to obtain the graph of h (in red). The function f is defined by f(x) = x^2. Write down the expression for h(x).

Solution

f(x) = x^2

the graph of x^2 is shifted 3 units to the left and 4 units downwards

if the function is shifted to the left we add inside the parenthses (x+a)

and if the function is shifted downwards we subtract outside the parenthses (x+a)-b

hence, h(x) = (x+3)^2 - 4