Quadratic formula, Algebra

Quadratic Formula

It is the final method for solving quadratic equations & it will always work.  Not only that, although if you can recall the formula it's a fairly simple procedure as well.

We can derive the quadratic formula through completing the square on the general quadratic formula in standard form.  Let's do that and we'll take it sort of slow to ensure all the steps are clear.

First, as already noted we ought to have the quadratic equation in standard form.  Next, we have to divide both sides by a to obtain a coefficient of one on the x2 term.

ax2 + bx + c= 0

x2 +( b/ a) x +(c /a)= 0

After that, move the constant to the right side of the equation.

                             x2 + (b/a) x =  -  c/ a          

 

Now, we have to calculate the number we'll have to complete the square.  Again, it is one-half the coefficient of x, squared.

                                (b /2a) 2= b2 /4a2

Now, add this to both of the sides, complete the square & get common denominators on the right side to simplify things up a little.

x2 + (b/a) x +b2/4a2  =b2/4a2  -(c/a)

(x+(b/2a))2 = b2-4ac/4a2

Now we may employ the square root property on this.

2492_Quadratic Formula.png

Solve out for x & we'll also simplify the square root a little.

2008_Quadratic Formula1.png

As a final step we will notice that we've got common denominators on the two terms and thus we'll add them up.  Doing this gives,

236_Quadratic Formula1.png

Thus, summarizing up, provided that we begin in standard form,

                      ax2 +bx + c = 0

and that's very significant, then the solution to any quadratic equation is,

149_Quadratic Formula2.png

Posted Date: 4/6/2013 4:11:16 AM | Location : United States







Related Discussions:- Quadratic formula, Assignment Help, Ask Question on Quadratic formula, Get Answer, Expert's Help, Quadratic formula Discussions

Write discussion on Quadratic formula
Your posts are moderated
Related Questions
my homework instructions are "solve by factoring" and one of the problems is 2x^2+9x=0

The city of Eden would like to put in a new street that runs parallel to Harrington Highway because of traffic issues. The equation of Harrington Highway is y = -2x + 7. What wil

We've dealt along with this function many times already. Now it's time to graph it. First, let's remember ourselves of the definition of the absolute value function. It is a pie

We desire to look at the graph of quadratic function. The most general form of a quadratic function is,                                                       f (x ) = ax 2 + bx

Now we need to discuss the new method of combining functions. The new way of combining functions is called function composition. Following is the definition. Given two functions


The last topic that we have to discuss in this section is the change of base formula. Most of the calculators these days are able of evaluating common logarithms & natural logar



A mountain has an elevation of 19,389 feet in 1918, the glacier on this peak covered 4 acres. By 2003 this glacier had melted to 1 acre. What was the yearlyrate of change and what