y= -x^2+bx+c has a maximum value of when x = 2
-
maximum value is when slope of parabola is zero (y ' = 0)
y ' = -2x+b=0
using value x=2 will reveal value of b, so b=4
but we still don't know value of c which shifts parabola vertically (along y axis) so
answer is no. we need more info.
in general N unknowns requires N unique conditions to solve a problem.
here N=2 ( unknowns were B and C) but only one condition was given.
EDIT,
since it was also revealed that maximum value of Y is 5
we can solve it completely:
5= -2^2+4*2+C
so
C=1
so finally:
y=-x^2 + 4x+1
y ' = -2x+b=0
using value x=2 will reveal value of b, so b=4
but we still don't know value of c which shifts parabola vertically (along y axis) so
answer is no. we need more info.
in general N unknowns requires N unique conditions to solve a problem.
here N=2 ( unknowns were B and C) but only one condition was given.
EDIT,
since it was also revealed that maximum value of Y is 5
we can solve it completely:
5= -2^2+4*2+C
so
C=1
so finally:
y=-x^2 + 4x+1
-
y= -x^2+bx+c
y(2) = -4 + 2b + c = 5
y' = -2x + b
-4 + b = 0
b = 4
-4 + 8 + c = 5
c = 1
y = -x^2 + 4x + 1
Edit: solution: a = -1 , b = 4 , c = 1 => y = ax^2 + bx + c => standard equation
y(2) = -4 + 2b + c = 5
y' = -2x + b
-4 + b = 0
b = 4
-4 + 8 + c = 5
c = 1
y = -x^2 + 4x + 1
Edit: solution: a = -1 , b = 4 , c = 1 => y = ax^2 + bx + c => standard equation