Writing an Equation in Vertex Form by Completing the Square We want to write an equation in vertex form y ax h k , by using a process called completing the square. We will start with the standard form of the quadratic equation, y ax 2 bx c and then rewrite the equation in vertex form. 2 EXAMPLE #1 Write y x 2 20 x 9 in vertex from. 1. Add 9 to both sides, so the constant is eliminated from the right hand side. y 9 x 2 20 x 9 9 y 9 x 2 20 x 2. Now complete the square on the right hand side. 2 2 1 1 2 Since b 20 , then b = 20 = 10 = 100 2 2 So completing the square, we must add 100 to both sides, because we are dealing with an equation. y 9 100 x 2 20 x 100 y 109 x 2 20 x 100 3. We also know how to write the right side of the equation in factored form. Again, we know b 20 , so 1 y 109 x 20 2 2 y 109 x 10 2 4. Now the equation is written in vertex form. y x 10 109 , with a vertex of ( -10, -109 ) Algebra 2 Chapter 1.7 2 EXAMPLE #2 Write y x 2 6 x 7 in vertex from. 1. Subtract 7 to both sides, so the constant is eliminated from the right hand side. y 7 x 2 6x 7 7 y 7 x 2 6x 2. Now complete the square on the right hand side. 2 2 2 36 1 1 6 a. Since b 6 , then b = 6 = = =9 4 2 2 2 b. So completing the square, we must add 9 to both sides, because we are dealing with an equation. y 7 9 x 2 6x 9 y 2 x 2 6x 9 3. We also know how to write the right side of the equation in factored form. Again, we know b 6 , so 1 y 2 x 6 2 y 2 x 3 2 2 4. Now the equation is written in vertex form. y x 3 2 , with a vertex of 3,2 Algebra 2 Chapter 1.7 2

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# Writing an Equation in Vertex Form