a quadratic equation

Question

let y = ax^2+bx+c be a quadratic equation with the following chateristics:

1. its maximum point is (-1,-1)

2. its y-intercept is -2

find a, b, and c

Answer 1

y = ax² + bx + c

 

-2 = a(0)² + b(0) + c = c

 

c = -2

 

-b/(2a) = -1 ⇒ b = 2a

 

-1 = a(-1)² + 2a(-1) - 2

 

-1 = a - 2a - 2

 

1 = -a

 

a = -1

 

b = 2a = 2(-1)

 

b = -2

 

y = -x² - 2x - 2

 

Test the answer against the conditions stated in the problem.