Question

Look down below for question:

Answer 1

Area of ABC : AB*AC/2

the maximum of the parabola is reached at x=-4/(2*(-1))=2 hence A is at (2,0) and B is at (2,(-2)^2+4*2+C)=(2,12+C)

C is the second root (x-intersect), which we can find :

determinant1 : D=16-4*(-1)*C=4(4+C) thus the second root is at x=
`(-4-√(4(4+C)))/(-2)=2+√(4+C)`

Hence the area of the triangle is
`AB*AC/2=(4+C)*(2+√(4+C)-2)/2=(4+C)√(4+C)/2=32` hence
`(4+C)√(4+C)=64` .

We remark that
`64=16*4=16*√(16)`

Hence 4+C=16 thus C=12