Chapter 1.3, Problem 35E

To determine

Tofind:The missing values in the table given below for $y=x^2$ .

$x$	$y$	Change $\left(\Delta y\right)$
$1$	$?$	$?$$?$$?$
$2$	$?$
$3$	$?$
$4$	$?$

Answer to Problem 35E

The complete table for $y=x^2$ is shown below:

$x$	$y$	Change $\left(\Delta y\right)$
$1$	$1$	$3$$5$$7$
$2$	$4$
$3$	$9$
$4$	$16$

Explanation of Solution

Given information:

The equation is $y=x^2$ and the table is:

$x$	$y$	Change $\left(\Delta y\right)$
$1$	$?$	$?$$?$$?$
$2$	$?$
$3$	$?$
$4$	$?$

Calculation:

Substitute 1 for $x$ in the given equation.

  $\begin{array}{c}y=x^2\\ y=1^2\\ y=1\end{array}$

Substitute 2 for $x$ in the given equation.

  $\begin{array}{c}y=x^2\\ y=2^2\\ y=4\end{array}$

Substitute 3 for $x$ in the given equation.

  $\begin{array}{c}y=x^2\\ y=3^2\\ y=9\end{array}$

Substitute 4 for $x$ in the given equation.

  $\begin{array}{c}y=x^2\\ y=4^2\\ y=16\end{array}$

The change $\left(\Delta y\right)$ for the values 1 and 4 is:

  $\begin{array}{c}\Delta y_1=y_2-y_1\\ =4-1\\ =3\end{array}$

The change $\left(\Delta y\right)$ for the values 4 and 9 is:

  $\begin{array}{c}\Delta y_2=y_3-y_2\\ =9-4\\ =5\end{array}$

The change $\left(\Delta y\right)$ for the values 9 and 16 is:

  $\begin{array}{c}\Delta y_3=y_4-y_3\\ =16-9\\ =7\end{array}$

So, the values of $\Delta y$ are $3$ , $5$ and $7$ .

Therefore, the complete table is given below:

$x$	$y$	Change $\left(\Delta y\right)$
$1$	$1$	$3$$5$$7$
$2$	$4$
$3$	$9$
$4$	$16$