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)
1 answer:
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
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