# Math Help - Ways of solving quadratic relations

1. ## Ways of solving quadratic relations

Since Im taking online classes, there is no teacher who can help me really out; I still dont know what Graphing with technology means, dont get the concept of factoring with uneven numbers and what the quadratic formula is, I also dont know . And this Assignment needs to be done soon . Help or explanations would be very nice :-)

The quadratic equation, can be solved by:

• Graphing with or without technology.
• Factoring

Solve the quadratic equation using all three techniques. Rank the techniques in the order in which you would use them to solve this problem. Explain why you chose that particular ranking and summarize the benefits of each method. Explanations, diagrams, examples, formulas and mathematical terminology should all be included in your solution. Be thorough!

2. 'Solving' a quadratic means finding it's roots - the x values for which the function = 0. i.e. you are solving for x:

$ax^2+bx+c=0\quad\text{where a,b,c are constants,}a\ne0$

You can re-arrage this formula by completing the square to solve for x, which is called the quadratic formula, and looks like:

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Now plugging values from a given quadratic into here will give you your two roots, whether tey be real,equal, or complex.

Obviously on agraph of a function, it's roots will be the x values where the function crosses the y-axis (f(x)=0).

Finally, factoring is the opposite of expanding, and is used to easily see the roots of a function in factorised form, by using the factor theorem.

3. Originally Posted by Serialkisser
Since Im taking online classes, there is no teacher who can help me really out; I still dont know what Graphing with technology means, dont get the concept of factoring with uneven numbers and what the quadratic formula is, I also dont know . And this Assignment needs to be done soon . Help or explanations would be very nice :-)

The quadratic equation, can be solved by:

• Graphing with or without technology.
• Factoring