How to Find the Vertex of a Parabola Equation

Someone new to algebra may find it difficult to find the vertex of a parabola equation. The vertex is the maximum or minimum point of a parabola defined by a quadratic equation. There are two main forms of a quadratic from which you must calculate the vertex: vertex form and standard form.

Instructions

Vertex Form

1. Write the equation in vertex form: y = a(x-h)^2+k.

2. Record the variable k as the y coordinate of the vertex.

3. Set x-k = 0 and solve for x. Record this x value as the x coordinate of the vertex.

4. Combine the x and y coordinates found in Steps 2 and 3. Record this value as your vertex (x,y).

Standard Form

1. Define the variables of the quadratic equation in the standard form: y = ax^2+bx+c.

2. Plug the variables "h", "b" and "a" into the equation h = (-b/2a). Record h as the x coordinate of the vertex.

3. Substitute h in the original equation in place of x, making the new equation y = ah^2+bh+c. Solve for y. Record this value as the y coordinate of the vertex.

4. Combine the coordinates from Steps 2 and 3 and record them as your vertex at point (x,y).

Tips & Warnings

• The "^" symbol indicates the following number is an exponent.

• Additional algebraic techniques, such as completing the square, may be necessary to get the equation into the correct format.

References

• Algebra Lab: Vertex of a Parabola