Identify the maximum of y=-3×2+8×+35?

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Answer 1 · 2018-03-23T05:48:54

#y_(max)=121/3#.

graph{-3x^2+8x+35 [-111, 111.1, -55.5, 55.5]}

#:. 3y=-9x^2+24x+105=-{9x^2-24x}+105#.

Completing the square of #9x^2-24x#, we have,

# 3y=-{(3x)^2-2(3x)(4)+4^2}+4^2+105#,

#=-(3x-4)^2+121#.

#:. y=-1/3(3x-4)^2+121/3#.

Since, #AA x in RR, (3x-4)^2 >=0#, multiplying this inequality by

#-1/3 < 0#, we will have,

#-1/3(3x-4)^2 <=0 rArr -1/3(3x-4)^2+121/3 <=121/3#.

#:. AA x in RR, y <=121/3#.

Consequently, #y_(max)=121/3#.