The Quadratic Formula

By: Samantha Wisner11:00-12:15 p.m.

*History of the Quadratic Formula*

The Quadratic Formula can be used to solve any algebraic equation.

*History of Quadratic Formula Cond.*

The first aspect that finally led to the quadratic equation was the recognition that it is connected to a very pragmatic problem.

*History of the Quadratic Formula Cond*

Around 700AD the general solution for the quadratic equation, this time using numbers, was devised by a Hindu mathematician called Brahmagupta.

*History of the Quadractic Formula Cond.*

It is known that the Egyptian wise men (engineers, scribes and priests) were aware of this shortcoming.

*First Step* The quadratic equation looks like this:

ax² + bx + c = 0 A, B, C are coefficients in the quadratic

equation. Need to solve for ‘x’.

*Second Step*Example Equation: x² − 4x − 5 = 0

Substitute A=1, B= -4, C=-5

*Third Step* Solve Equation in this formula:

*Fourth Step* Plug in the A, B, C in the Quadratic

Formula. A=1, B=-2, C=1 So for B plug in –2. For C plug in 1 and for

A plug in 1.

*Fifth Step*

*Sixth Step*

Substitute the variables in the equation and solve what is under the radical first.

*Seventh Step* Depending on the problem, you will need

two answers usually. In this problem, you just need one answer

since the number under the radical is 0.

*Eighth Step* The very last step you need to add the –2

(B variable) with the radical number and then divide by 2 in this case.

Since the variable (A) on the bottom was 1 then you would just divide by two.

*Ninth Step*

You would multiply the 2 and variable A which would be 1 in this problem.

*Tenth Step*

*As you can see the two different steps at the end*

Add and subtract to get the final two answers.

*Eleventh Step*When you substitute a number for the variable B and it is a negative number it becomes a positive number. As shown in the example.

*Twelfth Step* A more complex quadratic problem- You simplify the 3rd

step in the example to the –3 + and – radical 5. The last step, simplify the 2 and –8 after by 2…leaving a –4 on the bottom.

*Thirteenth Step* Leaving the five under the radical and

coming up with two answers 3+ radical 5 and 3 – radical 5.

These are some of the examples that will help to solve simple quadratic equations to the more complex ones.

Works Cited BBC - H2g2 - The History Behind The Quadratic

Formula." BBC - Homepage. H2g2's Researchers, 13 Oct. 2004. Web. 11 Oct. 2010.

<http://www.bbc.co.uk/dna/h2g2/A 2982567>. "Quadratic Formula." Math Homework Help – Math

tutor Software – Algebra Help - Teachers Choice Software. Web. 11 Oct. 2010. <http://www.teacherschoice.com.au/Maths_Library/Algebra/Alg_6.htm>.

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