What is the factorizaion of the polynomial graphed below? assuming it has no constant factor.

y = 0.96(x -√5)(x + √5).

Step-by-step explanation:

The two zeros of this polynomial are (0, 0) and (5, 0), and the vertex is (2.5, -6), all of this info readily available from the graph.

The standard equation of a vertical parabola with vertex at (h, k) is

y - k = a(x - h)^2, where the vertex is represented by (h, k).  Since we know that the vertex is (2.5, -6), the equation for the given graphed parabola is

y + 6 = a(x - 2.5)^2

Since the graph of this parabola goes through the origin, (0, 0), the following must be true if we substitute 0 for both x and y:

0 + 6 = a(0 - 2.5)^2, or 6 = a(6.25).  Thus, a = 6/6.25, or a = 0.96.

The equation of this polynomial must then be:

y + 6 = 0.96(x - 2.5)^2, which is satisfied by both (0, 0) and (5, 0).

This equation can be rewritten as

y = 0.96(x^2 - 5x + 6.25) - 6 = 0.96x^2 - 4.8x + 6 - 6, or just

y = 0.96x^2 - 4.8x.  We must factor this.  Factoring out 0.96, we get:

y = 0.96(x^2 - 5), which can be factored further:  

y = 0.96(x -√5)(x + √5).  This is the fully factored form of the polynomial.

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.