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 x-coordinate formula to find the value of x at the vertex. Once the x-coordinate is found, plug it into the original equation to find the y-coordinate.

  1. 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.

  2. Use the x-coordinate vertex formula

    The vertex formula for the x-coordinate 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 x-coordinate of 0.25.

  3. Plug the x-coordinate into the original equation

    Plug the x-coordinate of the vertex back into the original quadratic equation to find the value of the y-coordinate. 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).