What is the formula to find the vertex of a quadratic function?

Answers:

• The vertex of a quadratic function in the standard form ( f(x) = ax^2 + bx + c ) can be found using the following formulas:

  1. x-coordinate of the vertex: [ x = -\frac{b}{2a} ]

  2. y-coordinate of the vertex: To find the y-coordinate, substitute the x-coordinate back into the function: [ y = f\left(-\frac{b}{2a}\right) ]

  So the vertex ((h, k)) of the quadratic function ( f(x) = ax^2 + bx + c ) is given by: [ (h, k) = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right) ]

  Alternatively, if the quadratic function is in vertex form, ( f(x) = a(x-h)^2 + k ), then the vertex is simply ((h, k)).