Question

How do you write $f\left( x \right)={{\left( x+3 \right)}^{2}}-7$ in standard form?

Answer 1

Hint: Here in this question we have been asked to write the given quadratic expression $f\left( x \right)={{\left( x+3 \right)}^{2}}-7$ in the standard form. From the basic concepts of quadratic expression we know that the standard form is given as $a{{x}^{2}}+bx+c$ .

Complete step by step answer:
Now considering from the question we have been asked to write the given quadratic expression $f\left( x \right)={{\left( x+3 \right)}^{2}}-7$ in the standard form.
From the basic concepts of quadratic expression we know that the standard form is given as $a{{x}^{2}}+bx+c$ .
From the basic concepts of algebra we know that ${{\left( a+b \right)}^{2}}={{a}^{2}}+{{b}^{2}}+2ab$ .
By using this expansion we will have $f\left( x \right)={{x}^{2}}+9+6x-7$ .
Now we will further simplify this expression by performing arithmetic operations. After doing that we will have $f\left( x \right)={{x}^{2}}+6x+2$ .
Therefore we can say that the standard form of the given quadratic expression $f\left( x \right)={{\left( x+3 \right)}^{2}}-7$ will be given as $f\left( x \right)={{x}^{2}}+6x+2$ .

Note:
While answering questions of this type we should be sure with the functions concepts that we are going to apply in the process and the calculations that we are going to perform in between. This is a very simple and easy question and can be answered accurately in a short span of time. Very few mistakes are possible in this type of question. Someone can unfortunately make a mistake during the simplification and write it as
 $\begin{align}
  & f\left( x \right)={{x}^{2}}+9+6x-7 \\
 & \Rightarrow f\left( x \right)={{x}^{2}}+6x+3 \\
\end{align}$
which will lead us to end up having a wrong answer. So we should be very careful while performing calculations.