Why Use “Completing the Square”

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Presentation transcript:

Ch3/4 Lesson 8 Solve Equations by Completing the Square Max/Min Problems

Why Use “Completing the Square” “Completing the Square” is a process that converts a quadratic function that can not be factored to a form that can be solved algebraically Suppose we have the following trinomial If we complete the square, we end up with the expression on the right Can’t factor this… We end up with two answers in radical form

Practice: Solve for ‘x’ in exact form:

Ex: Solve by Completing the Square Bracket the first two terms! Divide the second term by 2 and square it! Purpose: Make the expression in the bracket into a perfect square! Take the negative square outside of the brackets! The trinomial becomes two equal binomials Now you can solve this equation by square rooting both sides:

Practice: Solve for “x” by CTS Bracket the first two terms! Factor out any coefficient for x2 Divide the second term by 2 and square it! Take the negative square outside of the brackets and multiply with coefficient in front! The trinomial becomes two equal binomials Solve for “x” by square rooting both sides

Ex: The height, “h” metres, of an infield fly ball “t” seconds after being hit is given by simplified formula : h = 30t – 5t2. How long after being hit is the ball at a height of 18 m?

Ex: The sum of two numbers is 80. Their product is 1500 Ex: The sum of two numbers is 80. Their product is 1500. Find the numbers There are two numbers, let ‘x’ and ’80 –x’ be the numbers Gather Information 80 minus the first number gives you the second nunber The product is 1500 The two numbers are 30 and 80

Ex: A gardener would like to build a pathway of equal width around a rectangular garden measuring 8 meters by 15 meters. If this doubles the total area, then what is the width of the pathway? x = –13.6912 is call an extraneous root.

Ex: The difference of two numbers is 10. The sum of their squares is 60. Find the numbers The second number is 10 more than the first Gather Information The sum of their squares is 60 The two sets of numbers are: