[tex] A=(6-x)(x+8)=6x+48-x^2-8x=-x^2-2x+48 [/tex]
[tex] -x^2-2x+48=-(x^2+2x-48)=-(x^2+2x+1-49)=-((x+1)^2-49)=-(x+1)^2+49 [/tex]
The maximum value of a quadratic function when it's written in the form [tex] f(x)=a(x-h)^2+k [/tex] is equal to [tex] k [/tex]
The maximum area is 49.
