Question

the function ( f ) is defined as follows.
( f(x) = 2x^2 - 5 )
if the graph of ( f ) is translated vertically upward by 4 units, it becomes the graph of a function ( h ).
find the expression for ( h(x) ).
note that the aleks graphing calculator may be helpful in checking your answer.

Explanation:

Step1: Recall vertical translation rule

For a vertical upward translation by $k$ units, $h(x)=f(x)+k$

Step2: Substitute $f(x)$ and $k=4$

$h(x)=(2x^2 - 5) + 4$

Step3: Simplify the expression

$h(x)=2x^2 - 5 + 4 = 2x^2 - 1$

Answer:

$h(x)=2x^2 - 1$