Describe A Quadratic Equation

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

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linear, quadratic, polynomial, rational, exponential, log

To increase your understanding of these, choose one equation of each type: linear, quadratic, polynomial, rational, exponential, and log. Plot each equation on the same graph. Discuss and compare the appearance of each graph. Describe the plot’s shape, the effect of any constants, and behavior for very large or very small x or y.

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