An expression is shown below.

f(x) = 4x2 + 8x - 5

part a: what are the x-intercepts of the graph of f(x)? show your work.

part b: is the vertex of the graph of f(x) going to be a maximum or minimum? what are the coordinates of the vertex? justify your answers and show your work

part c: what are the steps you would use to graph f(x)? justify that you can use the answers obtained in part a and part b to draw the graph.

Part A) The x-intercepts are the points (-2.5,0) and (0.5,0)

Part B) The vertex is a minimum and the coordinates are (-1,-9)

Part C) see the explanation

Step-by-step explanation:

we have

Part A: What are the x-intercepts of the graph of f(x)?

we know that

The x-intercepts are the values of x when the value of the function f(x) is equal to zero

so

For f(x)=0

Solve the quadratic equation

The formula to solve a quadratic equation of the form

is equal to

in this problem we have

so

substitute in the formula

therefore

The x-intercepts are the points (-2.5,0) and (0.5,0)

Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the coordinates of the vertex?

we know that

The quadratic equation represent a vertical parabola open upward (because the leading coefficient is positive)

therefore

The vertex represent a minimum

Convert to vertex form

Factor 4

Complete the square

Rewrite as perfect squares

> equation in vertex form

The vertex is the point (-1,-9)

Part C: What are the steps you would use to graph f(x)?

To graph f(x)

I need

1) The direction of the graph (Is a vertical parabola open upward)

2) The coordinates of the vertex (-1,-9) ( in this case is a minimum)

3) The x-intercepts  (-2.5,0) and (0.5,0)

4) The y-intercept

The y-intercept is the value of f(x) when the value of x is equal to zero

so

For x=0

The y-intercept is the point (0,-5)

Plot the points and draw the parabola

see the attached figure to better understand the problem

idk do it yourself or ask somebody idk stop going online asking for

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.