Question

100 POINTS 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

Answer:

see below

Step-by-step explanation:

f(x) = 5x^2 + 2x − 3

        (5x-3) ( x+1)

To find the x intercepts, set this equal to zero

0=  (5x-3) ( x+1)

Using the zero product property

5x-3 =0     x+1 =0

5x=3             x =-1

x = 3/5             x = -1     are the zeros

End behavior

x = -infinity

5 ( -infinity )^2

5 (infinity) = infinity

as x goes to negative infinity, f(x) goes to infinity

x = infinity

5 ( infinity )^2

5 (infinity) = infinity

as x goes to  infinity, f(x) goes to infinity

To plot the function, we need to plot the zeros ( or x intercepts) and the end behavior as well as the vertex to plot the graph