Question

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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)

Answer 1

A) factor f(x) are 3/5 and -1.

B) x-intercepts of the graph of f(x)  are (3/5, 0) and (-1, 0).

C)  The end behavior is explained by vertex of the graph which is (-0.2, -3.2)

D) The graph is symmetrical about x = -0.2. shown below

What is factorization?

Factorizing is a way of writing an expression as a product of its factors using brackets.

Given function is : 5x² + 2x − 3

A)5x² + 2x − 3

= 5x² + 5x-3x − 3

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

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

So, factors will be 3/5 and -1.

B) f(x)= 5x² + 2x − 3

The x-intercepts are when f(x) = 0.

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

C) The x-coordinate of the vertex is the midpoint of the zeros.

 midpoint= (3/5-1)/2

                =-0.2

To find the y-coordinate of the vertex, substitute the found value of x into the given equation:

f(-0.2)= 5(-0.2)² + 2(-0.2) − 3

=-3.2

So, the end behavior is explained by vertex of the graph which is (-0.2, -3.2)

D) By plotting the zeroes and the vertex of the f(x).

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

Thus,   the graph is symmetrical about x = -0.2.

Learn more about factorization here:

https://brainly.com/question/20293447

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