Presentation on theme: "Objective: To solve quadratic equations by completing the square."— Presentation transcript:
1 Objective: To solve quadratic equations by completing the square. Lesson 10.3-Solving Quadratic Equations by Completing the Square, pg. 539Objective:To solve quadratic equations by completing the square.
2 Finding the Square Root Some equations can be solved by taking the square root of each side.Square Root Symbol: √To solve an equation by taking the square root, you must rewrite the perfect square trinomials as a binomial square.
10 Ex. p²+ 12p = 13When solving a quadratic equation using the Square Root property you must have a Perfect Square Trinomial. If you don’t then you must create one.
11 Creating a Perfect Square Trinomial Ex. x²+ 6x + cx²+ 6x + 3²x² + 6x + 9(x + 3)²Take half of the middle term And ADD its SQUARE
12 Ex. m² - m + c m² - m + (-½)² (m - ½)² Take half of the middle term And ADD its SQUARE
13 Try these…. Find the value that makes each trinomial a perfect square Try these…. Find the value that makes each trinomial a perfect square. Then write the binomial square.t² - 24t + cb² + 28b + c3. y² + 40y + c4. g² - 9g + cThis method is called Completing the Square
14 Steps for Completing the Square Step 1: Make sure the leading coefficient is ONE, if not, DIVIDE the entire equation by the leading coefficient.Step 2: Isolate the variable terms ax² + bxStep 3: Find b/2 and ADD its square to both sides.Step 4: Solve by using the SQUARE ROOT PROPERTY.
15 Ex. 2: Solve each equation by completing the square Ex. 2: Solve each equation by completing the square. Round to the nearest tenth if necessary.1. x² + 6x + 3 = 0
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