Question

Complete the following table of values and plot the graphs on the same set of axes. Use values of $- 8$ to $12$ on the y-axis.

	$x$	$- 3$	$- 2$	$- 1$	$0$	$1$	$2$	$3$
$a$	$y = x^{2} + 1$
$b$	$y = x^{2} + 3$
$c$	$y = x^{2} - 2$
$d$	$y = - x^{2} + 1$
$e$	$y = 3 - x^{2}$

Accepted Answer

If $x = - 3$ , then $y = x^{2} + 1 = {(- 3)}^{2} + 1 = 10$

Similarly, if we substitute the values of $x = \{- 3, - 2, - 1, 0, 1, 2, 3\}$ , we obtains the values of $y$ as below for the given quadratic equations.

$x$ $- 3$ $b$ $- 1$ $0$ $1$ $2$ $3$

$a$ $y = x^{2} + 1$ $10$ $5$ $2$ $1$ $2$ $5$ $10$

$b$ $y = x^{2} + 3$ $12$ $7$ $4$ $3$ $e$ $y = 3 - x^{2}$ $12$

$c$ $y = x^{2} - 2$ $7$ $2$ $- 1$ $- 2$ $- 1$ $2$ $7$

$d$ $y = - x^{2} + 1$ $- 8$ $- 3$ $0$ $1$ $0$ $- 3$ $- 8$

$e$ $y = 3 - x^{2}$ $- 6$ $- 1$ $2$ $3$ $2$ $- 1$ $- 6$

Now, plotting the points denoted as above on the same set of axes, we obtain the graph as given below.

Karen Morrison and Nick Hamshaw Solutions for Exercise 1: Exercise 18.1

Karen Morrison Mathematics Solutions for Exercise - Karen Morrison and Nick Hamshaw Solutions for Exercise 1: Exercise 18.1

Questions from Karen Morrison and Nick Hamshaw Solutions for Exercise 1: Exercise 18.1 with Hints & Solutions

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