Question

The function h is defined as follows. If the graph of h is translated vertically downward by 4 units, it becomes the graph of function f.

Answer 1

So here we have the function:

`h(x)=-3x^2+4`

If the graph of h is translated vertically downward by 4 units, it becomes the graph of function f.

Remember that when we translate vertically downward the graph of a function "c" units, that could be represented if we sum or substract "c" to the function. In this case the function is being translated 4 units down, so we should substract "4" to the function h. Therefore, our function f will be:

`\begin{gathered} f(x)=h(x)-4 \\ f(x)=-3x^2+4-4 \\ f(x)=-3x^2 \end{gathered}`