Idon’t know how to solve this for questions #3 and #5?

Step-by-step explanation:

3) h(x) = -4x^2 + 24x -41

a)

a = -4, b = 24, and c = -41

Vertex formula: x= –b/2a

x = -24 /2(-4)

x = -24/-8

x = 3

Plug in x = 3 to find y:

= -4(3^2) + 24(3) - 41

= -4(9) + 72 - 41

= -36 + 72 - 41

= -5

Vertex (3, -5)

b) The axis of symmetry

The x-coordinate of the vertex is the axis of symmetry of the parabola

x = 3

Step-by-step explanation:

#3

Let's rewrite the equation in vertex form.

h(x) = -4x^2 + 24x - 41

h(x) = -4(x^2 - 6x) - 41

h(x) = -4(x^2 - 6x + 9) - 41 + 36

h(x) = -4(x - 3)^2 - 5

The vertex form is

f(x) = a(x - h)^2 + h

where point (h, k) is the vertex.

We see that h = 2, and k = -5.

The vertex is (3, -5).

The axis of symmetry is x = h.

The axis of symmetry is x = 3.

#5

The remainder theorem states that the remainder of synthetic division of the polynomial by x - c is the same as the value of the function evaluated at c. Here, c = 5, so we do the synthetic division using 5.

  5|       1   9   15       -15         20

           5   70    425    2050

            1    14  85    410     2070

The remainder is 2070. That means that

f(5) = 2070

If k is a zero of function f, then f(k) = 0. Here, f(5) is not zero, so 5 is not a zero of the function.

answer: 5000

step-by-step explanation:

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.