# Basics of Completing the Square

• Completing the square is a method used to solve quadratic equations, convert quadratic functions to vertex form, and understand the graph of a quadratic function.

• It involves rearranging a quadratic equation to create a perfect square trinomial from the quadratic and linear terms.

# Steps to Complete the Square

• Begin by ensuring your quadratic equation is in the form ax^2 + bx + c = 0. If ‘a’ is not 1, divide every term by ‘a’ to make it 1.

• Move the constant term (c) to the other side of the equation.

• Take half of the coefficient (number) of the ‘x’ term (b), square it, and add it to both sides of the equation.

• The left side of the equation can now be written as a binomial squared: (x + h)^2, where h is half of the original ‘b’ value.

• Solve for ‘x’ by taking the square root of both sides, remembering to consider both the positive and negative square roots.

# Key Points to Remember

• Completing the square only works directly on quadratics in the form x^2 + bx + c = 0. If the coefficient of x^2 is not 1, it must be made 1 by dividing every term by that coefficient.

• After rearranging the equation, the left side becomes a perfect square: (x + h)^2.

• Once the equation is in the form (x + h)^2 = k, solve for ‘x’ by taking the square root of both sides. Remember to consider both the positive and negative square roots.

• This method is particularly useful for determining the turning point (vertex) of a quadratic function, and for sketching its graph. The vertex form of a quadratic is y = a(x - h)^2 + k where (h, k) are the coordinates of the vertex.