Question

How do you approximate the value of a quadratic expression \[2{x^2} - 3xy + x\] at $\left( {1,1} \right)$ ?

Answer 1

Hint: In the given question, we are required to approximately calculate the value of a quadratic expression given to us as \[2{x^2} - 3xy + x\] at $\left( {1,1} \right)$. The given statement of the question means that we have to put in the value of variables x as $1$ and the value of y as $1$ and find the value of the quadratic expression provided to us.

Complete step-by-step answer:
So, in order to find the value of the quadratic function given to us in the question itself, we need to plug in the values of variables as specified in the question.
So, \[2{x^2} - 3xy + x\]
Putting in x as $1$ and y as $1$, we get,
 \[ \Rightarrow 2{\left( 1 \right)^2} - 3\left( 1 \right)\left( 1 \right) + \left( 1 \right)\]
 \[ \Rightarrow 2 - 3 + 1\]
 \[ \Rightarrow 0\]
Hence, we get the value of the expression \[2{x^2} - 3xy + x\] for the given values of x and y as \[0\] by replacing the variables with the values as specified in the question itself.
So, the correct answer is “0”.

Note: Such questions that require just simple change of variable can be solved easily by keeping in mind the algebraic rules such as substitution and transposition. Substitution of a variable involves putting a certain value in place of the variable. That specified value may be a certain number or even any other variable. Knowledge of basic and simple algebraic rules and operations such as substitution, addition, multiplication, subtraction and many more like these can be of great significance in tackling these kinds of questions. A thorough understanding of functions and its applications can be of great significance.