Mathematical+Reflections,+64+0910

S.M May 8, 2010 Big Idea: Equations can be used to model real things. Essential Question: How do I create and solve equations?

Mathematical Reflections 4 ** 1. Describe some general strategies for solving linear equations. Give examples that illustrate your ideas. ** One and the most obvious strategy for solving any equation is by tracing a graph or table. The symbolic method is also a vacant option. The point of it is to have x by itself on one side of the equal sign and the rest on the other. For Example: 12+5x=2-4x -12 +12+5x=2-4x -12 5x=-12+2-4x 5x +4x =-12+2-4x +4x 5x+4x=-12+2 9x=-10 9 /9 x=-10 /9 x=-10/9

One way to solve this equation is by graphing it or making a table, then finding the x-intercepts or the roots. Another way is by turning the expanded form into factored form, and applying the 0 property of multiplication.
 * 2. a. What general strategies can you use to solve quadratic equations of the form ax^2+bx=0? **

The 0 property of multiplication will work, but first you have to change it to factored form. If a=1, b=6, and c=9, then the equation would look like this: x^2+6x+9=0. If you convert it into factored form, it changes into (x+3) (x+3). The x in the first pair of parenthesis will become -3, and same for the second pair, so -3 is the root or the solution.
 * b. Will the strategies you described in part a work for solving quadratic equations of the form ax^2+bx+c=0? Use an example to help explain your answer. **

For a graph like this you would have to find the x-intercept. It will be the x value when y is 0, which is also the solution since in this equation, the y is 0.
 * 3. a. How could you solve a linear equation of the form mx+b=0 by using a graph? **

You would graph each side of the equation, so ax+b=0 and cx+d=0. You would have to fide the two lines’ intersection point.
 * b. How could you solve a linear equation of the form ax+b=cx+d by using a graph? **

This equation will produce a parabola, so then you have to find the two x-intercepts or the roots of the parabola. There will be two possible solutions.
 * c. How could you solve a quadratic equation of the form ax^2+bx=0 by using a graph? **

In this investigation we learnt about methods for solving linear and quadratic equations.
 * Summary: **