Asap (30 points) & brainliest

use the function f(x) = 4x2 + 8x − 5 to answer the questions.

part a: completely factor f(x). (2 points)

part b: what are the x-intercepts of the graph of f(x)? show your work. (2 points)

part c: describe the end behavior of the graph of f(x). explain. (2 points)

part d: what are the steps you would use to graph f(x)? justify that you can use the answers obtained in part b and part c to draw the graph. (4 points)

Part A)

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

Part C) see the explanation

Part D) The graph in the attached figure

Step-by-step explanation:

we have

Part A: Completely factor

Factor 4 leading coefficient

Complete the square

Rewrite as perfect squares

Part B: 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 is equal to zero

we have

For f(x)=0

Move the constant to the right side

take the square root both sides

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

Part C: Describe the end behavior of the graph of f(x)

we have

This is the equation of a vertical parabola in vertex form

The parabola open upward

The vertex represent a minimum

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

The function is decreasing in the interval (-∞,-1)

The function is increasing in the interval (-1,∞)

The domain is the interval (-∞,∞)

The range is the interval [-9,∞)

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

step 1

Plot the vertex

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

step 2

Plot the y-intercept

The y-intercept is the value of the function when the value of x is equal to zero

For x=0

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

step 3  

Plot the x-intercepts    

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

using a graphing tool

join the points to graph the parabola

see the attached figure

answer: sorry

step-by-step explanation: can you tell me pls how to find the rational of two integers

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.