Question

The function f is defined as follows.f(x) = -2x2-5If the graph of fis translated vertically upward by 3 units, it becomes the graph of a function h.Find the expression for h(x)

Answer 1

Answer: $h(x)\text{ = -2x}^2-\text{ 2}$

Explanation:

Given:

f(x) = -2x² - 5

To find:

The function for h(x) after a vertical translation of 3 units upwards

Translation rules:

$\begin{gathered} f(x\text{ + a\rparen = translation to the left} \\ f(x\text{ - a\rparen: translation to the right} \\ f(x)\text{ + b: translation upward} \\ f(x)\text{ - b: translation downward} \end{gathered}$

From the above, a translation of 3 units upward will involve adding 3 units to the function of f(x)

$\begin{gathered} h(x)\text{ = f\lparen x\rparen + 3} \\ h(x)\text{ = -2x}^2\text{ - 5 + 3} \\ \\ h(x)\text{ = -2x}^2\text{ - 2} \end{gathered}$