College Algebra Math

Question

The number of board feet in a 16 foot long tree is approximated by the model  where y is the number of feet and x is the diameter of the log.

How many board feet are in a log with diameter 6.5 inches?                Round to the nearest whole board. 

What is the diameter that will produce the minimum number of board feet?   Round to 4 decimal places. 

please help me

Answer 1

For the first question, you just need to plug it the value of the diameter for x. So y=.77*(6.5)^2-1.32*6.5-9.31

And y=the number of board feet.

For part 2, I know from looking at the equation that the parabola goes below the x-axis. But, board feet can't be negative, so you need to find the x value where y=0. You can use the equation x= (-b ± √(b²-4*a*c))/2a

(the quadratic formula, where a=.77, b=-1.32, c=-9.31) to find the x values where y=0. You will get two answers, but you know you can't have a negative diameter, so only the positive one works.

A good way to check your answers would be to plug this equation into a graphing calculator or the website desmos