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# mat 117 week 7 DQ's 4 different explanation

CSU - Dominguez hills

GPA 3.0

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Date Created: 11/16/15

Week 7 DO 1 Due Day 2 Please post a 150 300 word response to the following discussion question by clicking on Reply How do you know if a quadratic equation will have one two or no solutions How do you find a quadratic equation it you are only given the solution Is it possible to have different quadratic equations with the same solution Explain Provide your classmate s with one or two solutions with which they must create a quadratic equation Consider responding to your classmates by creating an equation from their solutions Show that your equation should yield the appropriate number of solutions If other equations exist with the same solution provide the alternate equation and provide an explanation You may want to view responses to the solutions you posted and guide your classmate s if necessary Explanation 1 How do you know if a quadratic equation will have one two or no solutions The square root of a positive number is also some positive number So in the numerator of the quadratic formula we will get two values b the square root and b the E i 4E TiZI square root So when we get two solutions Bquot2 4ac is zero The square root of zero is zero 80 in the numerator we get b 0 and b 0 But both of these are equal to bSo when bquot2 4ac we only get one solution If the equation is negative then you will have no solution because you cannot square any real number and get a negative number How do you find a quadratic equation it you are only given the solution One way to find solutions from the equation is to factor it For example solving Xquot2 5X 6 factor it x2x3 x2 O or x3 0 Solving these we get x2 or x3 Is it possible to have different quadratic equations with the same solution Yes it is possible to have to different equations with the same solutionFor example Solution x 1 or x 6 Equation x1x6 0 which gives xquot27x6 Explanation 2 A quadratic equations will have one solution the vortex or like the very tip of the curvewhere tangent 0 intercepts with the x axis 2 solutions where the formula intercepts the x axis at two positions 0 solution where the curve doesn39t touch the x axis An example to nd the quadratic equation if only given one solution is xquot2 6x 9 0 x3x3 0 x3 Is it possible to have the same solution for two equations example axquot2 bx c y and axquot2 bx c y I really am not comfortable with this question or making an equation to solve So i will wait until i see some more examples before I try it Explanation 3 To determine if a quadratic equation will have one two or no solutions we must first find the discriminant If bquot2 4ac0 then there is only one solution If it is gt0 then there are two If it is lt0 then there are no solutions To find a quadratic equation when only the solution is given you can recreate the equation as follows y kXaXb To recreate the equation all one needs to do is replace the variables a and b with the solutions that are given Yes it is possible for two different quadratic equations to have the same solution because the variable k in ykXaXb can have different values Examples X4 X3 X5X7 Explanation 4 How do you know if a quadratic equation will have one two or no solutions By looking at the discriminant D bquot2 4c When D gt O Px has two distinct real roots When D O Px has two coincident real roots When D lt O Px has no real roots How do you nd a quadratic equation if you are only given the solution Let39s say we are given the roots x a and x b then the quadratic equation is xaxb 0 Is it possible to have different quadratic equations with the same solution Yes it is Again if we have the roots x a and x b then we can have CXaxb 0 where C is a constant So multiplying with a constant does not change the roots Provide your classmate39s with one or two solutions with which they must create a quadratic equation Find a quadratic equation that has roots x 2 and x 5 x2x5 O Find a quadratic equation that has two roots at x 1 x1x1 0 Week 7 DO 2 Due Day 4 Please post a 150 300 word response to the following discussion question by clicking on Reply Quadratic equations may be solved by graphing using the quadratic formula completing the square and factoring What are the pros and cons of each of these methods When might each method be most appropriate Which method do you prefer Explain why Explanation 1 If graphing is used to solve a quadratic equation you have to choose a number of values for xcoordinates to calculate the ycoordinates or vice versa This process can take a lot of time and it is hard to determine what your solution is by looking at the graph if the solution is not a whole number Example x12 x067 If the quadratic formula is used to solve a quadratic equation this method can be used to solve any quadratic equation It gives solution whether the solution has simple or complex numbers Again process can be lengthy If completing the square is used to solve a quadratic equation this method can used for solving and quadratic but may sometimes be challenging if the quadratic does not have a perfect square binomial Example xquot2 14x 4 Factoring can be used to solve quadratic only if the equation is factorable Example 6xquot2 15x 0 My rst method for solving quadratic equations will be Factoring only if the equation factors easily My second method will be using the Quadratic formula if the equation cannot be factored Explanation 2 Solving quadratic equations by graphing is probably the most lengthy and dif cult process because you have to nd the variables to graph It does however give you a visual and if the line is straight then you know you did the problem correcty Solving it by completing the square is also lengthy but e icient because you can check your work by plugging in the square roots you came up with Factoring is the easiest option and most used because you complete the process by factoring the variables in I prefer factoring over the rest of the options because I am not going to waste my time doing a graph if I don t have too I also don t have the materials to do so lying around and completing the square is almost backwards to me None of these options are wrong to nd the correct answer it just depends on individual preference Explanation 3 The single sure and easy way to solve them is using the quadratic formula Just substitute do a wee bit of arithmetic and you39re done It39s main downside is that sometimes the answer can be seen a little more quickly with factoring Factoring is second best Some quadratics have factors that just jump out at you but the best part about factoring is that when they do just jump out at you most people kind of feel they got the answer for quotfreequot without having to work for it and folks just love that feeling For that reason it doesn39t SEEM as hard as using the Quadric formula and doing the wee bit of arithmetic does Folks like the feeling of easy It39s main downfall is that outside of tests and homework the world is filled with Quadratic formulas that are HARD HARD HARD to factor Completing the square is fairly pointless as it is harder than just using the Quadratic formula It39s error prone because you have to remember several steps and get them right It39s pretty pointless And it39s kind of just a specialized factoring approach Graphing is a last resort It is handy for when you have little to work with perhaps the information is buried in a word problem or just need an approximate answer The Quadratic formula is absolutely the best except for the simplest and most memorable of equations I mean if I have to factor xquot2 1 I39m doing it with factoring but only because I39ve known the answer for decades Anything that doesn39t just jump out I39m using the Quadratic formula Explanation 4 A pro concerning graphing is that you can quickly input numbers into a graphing calculator to get an answer However the con of this is that the answer you get is a roundabout answer A pro concerning the quadratic formula is that the process is very exact The con of this would be that the process although exact may take a while to arrive at your answer A pro of completing the square is that it allows you to derive precise answers A con of this can be the amount of time it takes to solve using this method A pro of factoring is that it is the simplest method in my opinion A con of factoring would be how it may become confusing over time if you are needing to find answers for many different variables I would have to say my favorite method is factoring Factoring seems to fit my style of completing any algebra problem Plus it makes you use your brain in a different way in my opinion

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