![]() ![]() ![]() If Varsity Tutors takes action in response to Information described below to the designated agent listed below. Or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one This means that and, so the line of symmetry - which is the x-coordinate - is at. Now you can factor the quadratic to Perfect Square form, and subtract 4 from both sides to finish Vertex Form: So as you transform the parentheses on the left to match Vertex Form and add the +1 within parentheses to do so, also add 4 to the right hand side to stay balanced: Of course, you can't just add 1 - which will be multiplied by the coefficient of 4 - without accounting for it on the other side of the equation. , so if you add 1 within the parentheses you can treat it as a perfect square to match Vertex Form. Next, think of which Perfect Square quadratic you can form using the terms in parentheses. To do so, focus on the and terms first, pulling them aside and factoring out the common 4 so that you have your coefficient: The line of symmetry of a parabola is the x-coordinate of its vertex, so you can solve this problem by taking the given quadratic and converting to Vertex Form,, where is the vertex. This provides you with Vertex Form, so you can say that and, making the vertex and the Line of Symmetry just the x-coordinate of. Then you can factor the quadratic on the left into perfect square form, and subtract 3 from both sides to reset to 0: Since that +1 will be multiplied by a coefficient of 3, you should add 3 to the right side of the equation to match what you've done on the left: Of course, you cannot just add one within the parentheses without balancing the rest of the equation on both sides. Then note that the way to turn into a perfect square would be to add 1 to it to get to. To do that, separate those two terms from the -2 term, and then factor out the coefficient of 3: To get to that form, you will want to complete the square by looking at the and terms and determining which perfect square equation they belong to. Vertex form is, where is then the vertex. Note that solving for the x-coordinate of the vertex of a parabola also tells you its line of symmetry, so your job here is to put the quadratic into Vertex Form in order to find the vertex, which will give you the line of symmetry. ![]()
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