Express the function y = 2x^2 + 8x + 1 in vertex form.

 The vertex form of the given function is

Step-by-step explanation: We are given to express the following function in vertex form.

We know that the vertex form of a quadratic function is given by

where (h, k) is the vertex.

From equation (i), we have

Thus, the vertex form of the given function is

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.