College Algebra Math Quadratic formula

Question

Can someone please work this problem out for me so i can compare my answer with yours and also see where i messed up at with my calculations. Thank you

The number of board feet in a 16 foot long tree is approximated by the model y=0.77x2−1.32x−9.31 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. 

Answer 1

x=6.5

y = 0.77 * 6.5^2 - 1.32 * 6.5 - 9.31

= 0.77 * 42.25 - 1.32 * 6.5 - 9.31

= 14.6425

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Minimizing the quadratic function y = 0.77x^2 - 1.32 x - 9.31

A=0.77 B=-1.32 C=-9.31

The max MAYBE occurs at:

-B/(2a) = 1.32/(0.77*2) = 1.32/1.54

= 132/154

= 66/77

= 6/7

the extrema is 0.77 (6/7)^2 - 1.32 (6/7) - 9.31 = -9 and 6/7 = -69/7 <--- disqualified

0 = 0.77x^2 - 1.32 x - 9.31

0 = 77x^2 - 132x - 931

132 +or- sqrt ( 132^2 + 4(77)(931)) / [2*77]

= [132 +or- sqrt( 304172)] / 154

negative branch also results in negative measures

the minimum occurs at:

(132 + sqrt(304172))/154 which is APPROXIMATELY 4.438