From Factored Form to Vertex Form: (x + 5)(x + 4)
This article will guide you through the process of converting the quadratic expression (x + 5)(x + 4) from factored form to vertex form.
Understanding Vertex Form
The vertex form of a quadratic equation is given by:
f(x) = a(x  h)² + k
Where:
 a determines the direction and width of the parabola
 (h, k) represents the coordinates of the vertex
Steps to Convert

Expand the factored form:
(x + 5)(x + 4) = x² + 9x + 20

Complete the square:
 Take half of the coefficient of the x term (9/2), square it (81/4), and add and subtract it inside the expression:
x² + 9x + 20 = x² + 9x + 81/4  81/4 + 20
 Rewrite the first three terms as a perfect square trinomial:
(x + 9/2)²  81/4 + 20

Simplify:
(x + 9/2)²  1/4

Vertex Form:
The expression is now in vertex form:
f(x) = (x + 9/2)²  1/4
Identifying the Vertex
By comparing this equation to the general vertex form, we can see that:
 a = 1
 h = 9/2
 k = 1/4
Therefore, the vertex of the parabola represented by the equation (x + 5)(x + 4) is (9/2, 1/4).
Key Takeaways
 Converting from factored form to vertex form allows you to easily identify the vertex of the parabola.
 Completing the square is a crucial step in this process.
 Vertex form provides a clear understanding of the parabola's shape, orientation, and position on the coordinate plane.