A

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

i dont know sorry

step-by-step explanation: