Given the beam below:

$($PLEASE SHOW STEPS AND EXPLANTION FOR EVERY PART$)$

PART $1$

Using the x coordinate as shown. The equation of the bending moment $($M$)$ in segment AB is that of a$\_\_\_\_\_\_\_($Select from one the following$)$

Option A: curve of $2$nd degree that is concave

Option B: straight line with a positive slope

Option C: curve of $2$nd degree that is convex

Option D: curve of $3$rd degree that is convex

Option E: straight line with a negative slope

Option F: horizontal line

Option G: curve of $3$rd degree that is concave

PART $2$

The maximum positive moment within Segment AB is mostly near at$\_\_\_\_\_\_$lb$-$ft $($Select from one the following$)$

Option A: $180$

Option B: $64$

Option C: $116$

Option D: $244$

PART $3$

The point of inflection within AB occurs mostly near at$\_\_\_\_\_\_$ft from support A$.($Select from one the following$)$

Option A: $6\mathrm{.}7$

Option B: $3\mathrm{.}9$

Option C: $9$

Option D: $4\mathrm{.}5$