Let g(x) = -2x2 + bx + c be a quadratic function, defined everywhere, where b and c are constants. If x = 1 marks the location of one of the zeros of this quadratic function, and if the y-intercept of this function is at (0, 5), then use this information to name constant b.

Answer 1

g ( x ) = - 2 * x ^ 2 + b * x + c

For:

x = 0

y= 5

Then:

g( x ) = - 2 * 0 ^ 2 + 0 * x + c = 5

g( x ) = c = 5

c = 5

For:

x= 1

y = 0

g ( x ) = - 2 * 1 ^ 2 + b * 1 + c = 0

g ( x ) = - 2 + b + c = 0

g ( x ) = - 2 + b + 5 = 0

g ( x ) = b + 3 = 0

b = -3