Y=1/3x-2 what is the slope ans the y-intercept

In the equation for a line, y=mx+b, you will find both the slope and the y-intercept. The letter m is your slope, and the letter b is your y-intercept. So, looking at your line's equation, we have y = 1/3x - 2. With this being said, 1/3 is your slope, and -2 is your y-intercept. Does this make sense?

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