Quadratic Equation Definition

A quadratic equation is a polynomial of second degree in a single variable. It is expressed as

`ax^2 + bx + c = 0`

 In the above equation, a,b,c are constants where a!= 0.

The figure below shows the plot of a quadratic equation `y = ax^2 + bx + c `. The values of all the three coefficients are varied one by one, i.e. while a is varied, b,c remain fixed and so on.

Quadratic Equation

From the figure, we conclude that the graph of a quadratic equation is a parabola and a variation in the values of the 3 coefficients shifts the position of this parabola on the coordinate axis.

The different values of the coefficients have been demonstrated by 5 different colors. In the leftmost figure, for example, green color plot corresponds to the value of a = 1, b = 0, c=-1/2. Similar is the case for the rest of the figures.

vAnother figure shown below is a plot of a simple quadratic equation (another parabola) and the points where this graph intersects the x-axis is the solution to the quadratic equation:

`x^2 - 4x - 5 = 0`

Quadratic Equation

In Algebra, the use of Quadratic Equations is probably the most frequent event. Engineers, Mathematicians, and researchers cannot proceed with their calculations without using this equation. That is why, it is really important for you to develop a sound understanding of the concepts related to this equation.






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