Quadratic Equations: the Vertex Form

Fórmula do Vértice na Equação Quadrática

The steps to transform a quadratic equation from standard form to vertex form

First Part

The second part

The Conclusion

One example

Let’s use a specific quadratic equation as an example to demonstrate these steps. Start with this equation:

y = 2x² + 8x +

After completing the square for the equation y = 2x² + 8x + 6y, we have transformed it into the equivalent equation with the completed square term:

y = 2( x² + 4x + 4 ) − 2

The term that was added and subtracted is 4, which is (b/2a)². The vertex form of the equation, therefore, is:

y = 2( x + 2 )² − 2

In this form:

• h is −2 (since the term is x+2, and for h, the formula is x-h).
• k is −2 (the constant term that remains after completing the square and moving the constant term to the other side).

So the vertex of the parabola described by this equation is at the point (−2,−2)