Question

Using graph of f(x)=x^2 write an equation for the function that has a vertical shift of -5 and a horizontal shift of -1

Answer 1

To obtain a vertical shift, add the right side of the equation by the given shift. This means f(x) will become f(x)+a where a is the vertical shift. Thus, f(x) with a vertical shift of -5 is as follows:

$f(x)=x^2-5$

To obtain a horizontal shift, change x to x-b, where b is the horizontal shift. Thus, a graph with a horizontal shift of -1 is as follows:

$\begin{gathered} f(x)=\lbrack x-(-1)\rbrack^2-5 \\ f(x)=(x+1)^2-5 \end{gathered}$