Use the function f(x) = 2x2 − 5x + 3 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)

Step-by-step explanation:

Step 1:  Answer Part A

 ← Factored

Step 2:  Answer Part B

Set both factors to zero and then solve for x

← x - int

← x - int

Step 3:  Answer Part C

To find the end behavior, you need to examine the y-values as x goes to negative infinite and positive infinite.

Since this is a parabola, that means either both ends go to positive infinite or both ends go to negative infinite.  In this case, the leading coefficient is positive therefore, we know that this graph will have an end behavior of both positive and negative infinite in the x-values will go to positive infinite in the y-values.

Step 4:  Answer Part D

First, I would like to graph the x-intercepts which will give me the knowledge about where approximately the graph will be located.  Followed by that, I would like to find the y-intercept by setting all of the x values to 0 and getting that the y-int is (0, 3).  Next, I would like to find the vertex using the vertex formula.  Then, I would write little arrow's where the end behavior is supposed to end up at.  Finally, I would draw the line through the points to find the graph that I need to draw.

Step 5:  Answer Part E

Look at the attachment for the graph