how to find the vertex of a quadratic function @aibot
To find the vertex of a quadratic function, you can use the formula:
x = -b / (2a)
where a, b, and c are coefficients of the quadratic function in the form of ax^2 + bx + c.
Once you find the x-coordinate of the vertex using the formula, substitute it back into the quadratic equation to find the corresponding y-coordinate.
For example, if you have the quadratic function f(x) = 2x^2 + 4x + 1, you can find the vertex as follows:
a = 2
b = 4
x = -4 / (2*2) = -4 / 4 = -1
Substituting x = -1 back into the equation:
f(-1) = 2(-1)^2 + 4(-1) + 1
= 2 + (-4) + 1
= -1
So, the vertex of the quadratic function f(x) = 2x^2 + 4x + 1 is (-1, -1).