Find g(x), where g(x) is the translation 7 units up of f(x)=x2.

write your answer in the form m(x+a)2+b, where m, a, and b are integers.

g(x)=?

The process of transformation under translation means that the figure is simply change into another position. That is, the angles, the lengths or any other characteristic is unchanged except for the position of the figure in the Cartesian coordinate alone.
We are given the function in the form of:

f(x) = x^2

Which can also be written as:

y = x^2

Since the translation made is to move the figure 7 units up, then this means that the y coordinate is increased by 7. The given equation is a parabola pointing up with vertex at (0, 0). So moving it up would move the vertex at point (0, 7). The vertex of y is represented by the variable b, therefore b = 7 which further gives us the function:

y' = x^2 + 7

or

g(x) = x^2 + 7

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.