Question

the function f is defined as follows.
$f(x) = -2x^2 + 7$
if the graph of f is translated vertically upward by 3 units, it becomes the graph of a function g.
find the expression for $g(x)$.
note that the aleks graphing calculator may be helpful in checking your answer.

Explanation:

Step1: Recall vertical translation rule

A vertical upward translation by $k$ units transforms $f(x)$ to $f(x)+k$.

Step2: Substitute $k=3$ into the rule

$g(x) = f(x) + 3$

Step3: Plug in $f(x)$ expression

$g(x) = (-2x^2 + 7) + 3$

Step4: Simplify the constant terms

$g(x) = -2x^2 + (7+3) = -2x^2 + 10$

Answer:

$g(x) = -2x^2 + 10$