Lesson 5: 3-5 Completing the Square

1. How can you identify a quadratic expression that is a perfect square?
2. How can you make a geometric model for (a+b)^2=a^2+2ab+b^2?

Completing the Square

N.CN.7 Solve quadratic equations with real coefficients that have complex solutions.
F.IF.8.a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

SAT questions related to solving quadratics: 2-3-13,3-3-14,1-3-16,5-3-3,8-3-16,1-4-25; analyzing graphs: 3-4-12,8-3-11,8-4-19,6-3-11

To complete the square for an expression of the form x^2+bx, add the square of one half of the coefficient b to x^2+bx.

A train moving at 24 meters per second begins to decelerate at a rate of 2 meters per second per second. The distance it travels after beginning to decelerate is given by the equation d=-t^2+24t, where t is the number of seconds after the deceleration begins. Suppose you want to know how long it will take to travel 80 meters. Substitute 80 for d in the equation. You can solve the problem by completing the square and using the Square Root Property.

When discussing the steps for completing the square, emphasize that the coefficient of the quadratic term must be 1.

Remind students to think carefully about the difference between multiplying a quantity by 2 and squaring a quantity.

Have students solve the equation x^2+6x-40=0 by completing the square. Then have them discuss with a partner as many ways as they can to check their solutions.

McGraw Hill resources

McGraw Hill resources