Question

How do you find $h\left( 4 \right)$ for $h\left( n \right)=-2{{n}^{2}}+4$ ?

Answer 1

Hint: In this question we have been asked to find the value of $h\left( 4 \right)$ for $h\left( n \right)=-2{{n}^{2}}+4$ . This can be done by substituting the number $4$ in the place of $n$ in the given function $h\left( n \right)=-2{{n}^{2}}+4$ . By substituting and simplifying we will get the required answer. For simplifying we will perform some simple basic arithmetic calculations to reduce it.

Complete step by step solution:
Now considering from the question we have asked the value of $h\left( 4 \right)$ for $h\left( n \right)=-2{{n}^{2}}+4$ .
For that sake we will substitute $4$ in the place of $n$ in the given function $h\left( n \right)=-2{{n}^{2}}+4$ .
By substituting we will have $\Rightarrow h\left( 4 \right)=-2{{\left( 4 \right)}^{2}}+4$ .
Now we will simplify this expression. After simplifying we will have $\Rightarrow -2{{\left( 4 \right)}^{2}}+4=-2\left( 16 \right)+4$ .
Now we will further simplify this expression. After that we will have
$\begin{align}
  & \Rightarrow -2\left( 16 \right)+4=-32+4 \\
 & \Rightarrow -28 \\
\end{align}$
Therefore we can conclude that the value of $h\left( 4 \right)$ for $h\left( n \right)=-2{{n}^{2}}+4$ is $-28$

Note:
While answering this question we should be sure about the calculations we perform and the concept we apply while answering this question. This is a very simple and easy question, very few mistakes are possible and it can be answered in very less span of time. Similarly we can find the value of $h\left( n \right)$ for any value of $n$ simply by substituting and performing some simple basic arithmetic calculations to further simplify and reduce the expression. For example we can find the value of $h\left( 3 \right)$ by substituting $n=3$ in the expression we will have $\Rightarrow h\left( 3 \right)=-2{{\left( 3 \right)}^{2}}+4$ and for this we will perform simple basic arithmetic calculations to further simplify and after reducing we will have $\Rightarrow h\left( 3 \right)=-2{{\left( 3 \right)}^{2}}+4\Rightarrow -2\left( 9 \right)+4=-18+4\Rightarrow -14$ .