How Do You Find the Vertex of a Quadratic Function?
To find the vertex of a quadratic equation, determine the coefficients of the equation, then use the vertex xcoordinate formula to find the value of x at the vertex. Once the xcoordinate is found, plug it into the original equation to find the ycoordinate.

Determine the coefficients of the equation
After confirming that the given quadratic equation is in its common form of y = ax^2 + bx + c, identify the values of the coefficients a, b and c. For example, the quadratic equation y = 2x^2 – x + 4 has coefficients of a = 2, b = 1 and c = 4.

Use the xcoordinate vertex formula
The vertex formula for the xcoordinate is x = b / (2a). While paying attention to any negative signs, plug the appropriate coefficient values into the formula, and solve for x. The quadratic equation y = 2x^2 – x + 4 has an xcoordinate of 0.25.

Plug the xcoordinate into the original equation
Plug the xcoordinate of the vertex back into the original quadratic equation to find the value of the ycoordinate. The quadratic equation y = 2x^2 – x + 4 has a y value of 3.875 when the x value is 0.25. Thus, the vertex of this quadratic equation is (0.25, 3.875).