help!! help!! help!! please help..?

Question

take points A(7/2,0), B (0,7), C(-7/6,0) on the xy-plane. the parabola y = -x^2+ax+b is tangent to both lines BA and BC.

1) determine a and b
2) calculate the area of the domain bounded by the line BA, the parabola and the y-axis.

guys.. i dont want the answers i want to know how to solve this problem.. please HELP!! this is going to determine my future.

Answer 1

y = -x^2 + ax + b
y' = -2x + a
BA is y - 7 = (-7/(7/2))(x - 0) = -2x or
y = -2x - 7
CB is y - 7 = ((0 - 7)/(0 + 7/6))(x - 0) = -6x or
y = - 6x - 7
Solving BA and the general slope of the parabola,
y = -2x + a
y = -2x - 7
a = - 7
Solving BC and the general slope of the parabola,
y = -2x - 7
y = -6x - 7
gives x,y = (0,- 7) for the intersection of the parabola and BC

- 7 = -0^2 - 7*0 + b
b = -7

1) y = - x^2 - 7x - 7 = - (x^2 + 7x + 7)

The intersections of The parabola and BA are
y = - x^2 - 7x - 7 = -2x - 7
x^2 + 5x = 0
x = 0, -5
. . . 0
A = ∫ (- 2x - 7 + x^2 + 7x + 7)dx
. . - 5
A = (1/3)x^3 + (5/2)x^2 from - 5 to 0
A = (1/3)125 + (1/2)125 = 625/6 = 104.1667

Answer 2

dude i know this and i am 12.
should have been listening in class.

Answer 3

please try to do yourself,then write which can't be done by you.