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.
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
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)
To find the x-coordinate of the vertex of a quadratic function, you can use the formula:
x = -b / (2a)
In the equation y = x^2 + bx + c, we can see that the coefficient of x^2 is 1 (denoted by 'a'). So, in this case, a = 1.
Now, using the formula, we substitute a = 1:
x = -b / (2 * 1)
Simplifying this expression gives us:
x = -b / 2
Therefore, the equation for the function that relates the x-coordinate of the vertex to b is:
x = -b / 2