Question

the function h is defined as follows.
( h(x) = 5x^2 + 7 )
if the graph of h is translated vertically downward by 8 units, it becomes the graph of a function f.
find the expression for ( f(x) ).
note that the aleks graphing calculator may be helpful in checking your answer.

Explanation:

Step1: Recall vertical translation rule

For a vertical downward translation by $k$ units, $f(x) = h(x) - k$

Step2: Substitute $h(x)$ and $k=8$

$f(x) = (5x^2 + 7) - 8$

Step3: Simplify the expression

$f(x) = 5x^2 + 7 - 8 = 5x^2 - 1$

Answer:

$f(x)=5x^2 - 1$