Question

Question 4 (Essay Worth 10 points)

(07.03, 07.05 HC)
Use the function f(x) = 2x²-5x+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) HELP ASAP

Answer 1

Part A

`f(x)=(x-1)(2x-3)`

Part B

`(x-1)(2x-3)=0\\\\x=1, (3)/(2)`

So, the x-intercepts are
`(1,0)` and
`\left((3)/(2), 0 \right)`

Part C

As
`x \to \infty`,
`f(x) \to \infty` because the leading coefficient is positive.

As
`x \to -\infty`,
`f(x) \to \infty` because the degree is even and the leading coefficient is positive.

Part D

Plot the x-intercepts on the graph, and then find the value of
`f(x)` at
`x=(5)/(4)` (the midpoint of the two roots) to plot the vertex. Then, draw a curve through these three points that approaches infinity as
`x \to \pm \infty`