Solve Quadratic Equation Using The Vertex

Solving Quadratic Equations

Let's have a look at how we solve a quadratic equation:

x²-3x+2=0

The easiest way to solve them is to follow certain steps:

Step 1

Find two numbers where when they are multiplied together equal the firstnumber (a=1) multiplied by the third number (c=2). These two numbers when addedto each other must also equal the second number (b=-3).

In the above example, the solution is -2 and -1.
We can see that when added together the result is -3 and that when multiplied together, the result is 2

Step 2

Rewrite the original equation splitting the middle part into two using thenumbers which you found in step 1.

x²-x-2x+2=0

Step 3

Start to factorise both halves of the equation:

x(x-1)-2(x-1)=0

At this point you will know if you are going along the correct track if thefirst bracket is the same as the second bracket.

Step 4

Collect everything before each bracket and put it into one bracket andmultiply this bracket by that which is inside the identical brackets:

(x-1)(x-2)=0

Step 5

In order for the left side of the equation to be equal to 0, one of the twobrackets must equal 0. So either:

a.
x-1=0
x=1

b
x-2=0
x=2

Step 6

Check these answers:

1²-(3*1)+2=0
1-3+2=0
0=0

2²-(3*2)+2=0
4-6+2=0
0=0

Therefore the possible solutions for the above equation are confirmed to be 1 and 2

Video Lectures in Mathematics

These are video lectures. But free broadcast is available in USA only. 1. Introduction An introduction to the series, this program presents several mathematical themes and emphasizes why algebra is important in today’s world. 2. The Language of Algebra This program provides a survey of basic mathematical terminology. Content includes properties of the real number system and the basic axioms and theorems of algebra. Specific terms covered include algebraic expression, variable, product, sum

Math 203 Answers to Practice Questions 1-24

First, sorry I was not present for my office hour today. I will be on the third floor at 3:30 tomorrow. Now, answers to the first part of the review sheet: Text conventions: oo means infinity =/= is the "does not equal" sign ^ means exponent, i.e. 4^2 means 4 with a superscript, or exponent, of 2. _ means base, i.e. log_8 means log with a subscript, or base, of 8. sqrt means square root 1. Subtracting 4 from both sides, -|4x - 2|