Solving Quadratics By Completing the Square

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Solving Quadratic Equations by Completing the Square

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Presentation transcript:

Solving Quadratics By Completing the Square

Review Solve for x When you take the square root, You MUST consider the Positive and Negative answers.

Solve for x But what happens if you DON’T have a perfect square on one side……. You make it a Perfect Square Use the relations on next slide…

To expand a perfect square binomial: Short Cut To expand a perfect square binomial: We can use these relations to find the missing term….To make it a perfect square trinomial that can be factored into a perfect square binomial. Then

Make this a perfect square trinomial Take ½ middle term Then square it The resulting trinomial is called a perfect square trinomial, which can be factored into a perfect square binomial.

Solve by completing the square Make one side a perfect square Add a blank to both sides Divide “b” by 2 4. Square that answer. Add it to both sides Factor 1st side Square root both sides Solve for x Solve by completing the square 1.

Solve by completing the square Move constant to other side. Add a blank to both sides Divide “b” by 2 4. Square that answer. Add it to both sides Factor 1st side Square root both sides Solve for x Solve by completing the square 2.

Solve by completing the square Move constant to other side. Add a blank to both sides Divide “b” by 2 Square that answer. Add it to both sides Factor 1st side Square root both sides Solve for x Solve by completing the square 3.

Solve by completing the square Move constant to other side. Add a blank to both sides Divide “b” by 2 Square that answer. Add it to both sides Factor 1st side Square root both sides Solve for x Solve by completing the square 4.

Steps to solve Quadratics by completing the square: Move the constant to side by itself. Make the side (w/variables) a perfect square by adding a certain number to both sides. To calculate this number Divide “b” (middle term) by 2 Then square that answer Take the square root of both sides of eq Then solve for x

In a perfect square, there is a relationship between the coefficient of the middle term and the constant term.