Question

If the graph of the function f defined by f(x)= −2x^2+1 is translated vertically downward by 3 units, it becomes the graph of a function h. How can I find the expression for h(x)?

Answer 1

h(x) = -2x^2 -2

Explanation:

You know that translating the point (a, b) vertically downward by 3 units will make it be the point (a, b-3).

The same translation works on the point (x, f(x)), or when a=x and b=f(x). Translated downward by 3 units, the point becomes ...

(x, f(x) -3)

You want to name this (x, h(x)), so we have ...

h(x) = f(x) -3

h(x) = -2x^2 +1 -3 . . . substitute the expression for f(x)

h(x) = -2x^2 -2 . . . . . simplify