Solving Quadratics
Factoring
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To factor this quadratic equation you first Set the equation to zero. If the quadratic side is able to factor then you set each factor equal to zero. After x^2=-5x-6 you move all terms to one side. You then factor x^2+5x+6=0 to (x+3)(x+2)=0. You then set each factor to zero and solve and you get x=-3 and x=-2.
Completing the square
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You first have to move the right side. You have to find half of b, which means b over 2. You then have to find b over 2 and square it so in this equation its 3^2=9. You then have to add b over 2 squared to both sides of the equation. You factor the quadratic side so its now (x+3)(x+3)=20. You then write it in perfect square form so its (x+3)^2=20. You take the square root of both sides and then solve for x.
Quadratic Formula
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Any quadratic equation of the form ax^2+bx+c=0, where a=0 can be solved for both real and imaginary solutions is to the right and is called the quadratic formula. First you use the numbers in the equation to get you a, b, and c which is 1, 6, and -11. You then put these values into the quadratic formula. You then start to simplify down until you radical is one number. You then also simplify the radical and you get your answer.
Reflection
In this investigation I learned how to solve quadratics. I learned how to factor an equation, complete the square of an equation, and also learned how to solve quadratics with using the quadratic formula. I also learned that with these equations I can find x- intercepts easier and make a graph with the equation.
Photo used under Creative Commons from Keith Allison