Use the function f(x) = 2x2 − 3x − 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. (I don't think you actually have to draw it though) (4 points)

see below

Step-by-step explanation:

A:  2x² - 3x - 5

    (2x - 5)(x + 1)

B:  Set the factored equation equal to zero and solve for x.

(2x - 5)(x + 1) = 0

2x - 5 = 0

2x = 5

x = 5/2

x + 1 = 0

x = -1

The x-intercepts are 5/2 and -1

C)  To find the end behavior, you need to look at the term in the unfactored equation with the highest exponential number.  For this equation, that is 2x².  Since the exponent is positive,  both ends of the graph will point in the same direction.  Because the leading coefficent is positive, the graph will point upwards.  The end behavior of the graph is that as the x-values approach both ∞ and -∞, the function approaches ∞.

D)  Since we know that the x-intercepts are 5/2 and -1, you can plot these points.  You also know that the graph will be in an upward U shape.  Plug in  a couple x-values and plot them to make the graphing of the equation more accurate.

step-by-step explanation:

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