Question

For a graph of the equation
y = x^2 + bx + c,
the x-coordinate of the vertex is a function of b. Write an equation for the function.

Answer 1

if the vertex is x^2 then i'm pretty sure the equation is

f(b)= "the square root of"(bx+c-y)

but don't quote me on that

its just an educated guess
you definately need a second opinion

Answer 2

for the equation the way you stated it as
y = x^2 + bx + c
the x-coordinate of the vertex would be -b/2

for the more general case of a quadratic function in the form
y = ax^2 + bx + c
it would be -b/(2a)