Question

Do we plot the graph of a quadratic equation or a quadratic polynomial? Take a suitable example to support your answer.

Answer 1

Hint: The main difference between an equation and a polynomial is that an equation is said to be a mathematical statement that asserts the equality between two expressions and are separated by “=” , whereas a polynomial is an expression comprising of a finite number of terms and each term is a product of a constant and one or more variables raised to some non-negative, integral powers.

Complete step-by-step answer:
To understand the difference between a quadratic equation and a quadratic polynomial ,we take example of \[{x^2} + 2x + 2 = 0\] which is a quadratic equation because it consists of an equality between two expressions \[{x^2} + 2x + 2\] and 0 whereas if we consider only the expression \[{x^2} + 2x + 2\] then we say that it is a quadratic polynomial as it has no equality and all the terms are product of a constant and variables with non zero powers
We can draw graphs of quadratic equations and not for quadratic polynomials. On one side where a quadratic equation represents a parabola, a quadratic polynomial on the other side is just an expression comprising of sum of terms only
For instance: \[y = {x^2} - 2x - 3\] is a quadratic equation which represents an upward parabola \[y + 4 = {\left( {x - 1} \right)^2}\]with vertex at \[\left( {1, - 4} \right)\]
 

We can plot graphs of the polynomials only if and only if they are written in the form of functions. Otherwise, there is no sense of plotting their graph, but on the contrary, all the equations can be represented graphically.

Note: Unlike the polynomials, equations are not bounded up to certain terms. An equation can consist of trigonometric, logarithmic, hyperbolic, inverse trigonometric, exponential and many more, kind of terms. But only on the condition that it contains equality or an inequality sign between the two expressions.