Question

Writing an equation for a function after a vertical translation

Answer 1

g(x) = -2x² - 1

Step-by-step explanation:

If we have a function g(x) = f(x) - c, we can say that g(x) is f(x) translated c units down.

So, if g(x) is f(x) translated 4 units down, we get

g(x) = f(x) - 4

Now, we can replace f(x) = -2x² + 3 on the equation to get

g(x) = -2x² + 3 - 4

g(x) = -2x² - 1

Therefore, the expression for g(x) is

g(x) = -2x² - 1