Question

the function h is defined as follows.
h(x)=4x² +6
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.
f(x) =

Explanation:

Step1: Recall vertical translation rule

For a function \( y = h(x) \), a vertical translation downward by \( k \) units gives \( y = h(x)-k \). Here, \( k = 8 \) and \( h(x)=4x^{2}+6 \).

Step2: Apply the translation to \( h(x) \)

Subtract 8 from \( h(x) \): \( f(x)=h(x)-8=(4x^{2}+6)-8 \).

Step3: Simplify the expression

Simplify \( (4x^{2}+6)-8 \): \( 4x^{2}+(6 - 8)=4x^{2}-2 \).

Answer:

\( f(x)=4x^{2}-2 \)