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)?

  h(x) = -2x^2 -2

Step-by-step 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

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have