Use the function f(x) = 5x² + 2x-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)

Factorization in mathematics is dividing a large number into smaller ones that, when multiplied together, give you the original number. Factorization is the division of a number into its factors or divisors.
For instance, the factorization of the integer 12 might appear as 3 times 4.

Function: f(x) = 5x² + 2x-3.

a) Completely factor f(x)

f(x) = 5x² + 2x-3.

= 5x² + 5x-3x − 3

= 5x(x+1)-3(x+1)

=(5x-3)(x+1)

f(x)=3/5 and -1.

b)The x-intercepts of the graph of f(x):

f(x) = 5x² + 2x-3.

At f(x) = 0, the x-intercepts are present.

Therefore, x-intercepts are (3/5, 0) and (-1, 0).

c) The end behavior of the graph of f(x):

f(x) = 5x² + 2x-3.

The middle of the zeros is the vertex's x-coordinate.

=-0.2

Find the y-coordinate of the vertex, and substitute the found value of x into the given equation:

f(-0.2)= 5(-0.2)² + 2(-0.2) − 3

=-3.2

d)The steps you would use to graph f(x):

The axis of symmetry is the x value of the vertex.

Therefore, the graph is symmetrical at about x = -0.2.

To learn more about factorization, refer to:

brainly.com/question/20293447

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