Complete the table of values for the relation y = x2 + 2x + 3 for the range −2 × 5.

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To complete the table of values for the relation $y = x^2 + 2x + 3$ for the range $-2 \le x \le 5$ , we will substitute each integer value of $x$ from $-2$ to 5 into the equation to find the corresponding $y$ value.

Calculate $y$ for each $x$ value.
For $x = -2$ :
$y = (-2)^2 + 2(-2) + 3 = 4 - 4 + 3 = 3$
For $x = -1$ :
$y = (-1)^2 + 2(-1) + 3 = 1 - 2 + 3 = 2$
For $x = 0$ :
$y = (0)^2 + 2(0) + 3 = 0 + 0 + 3 = 3$
For $x = 1$ :
$y = (1)^2 + 2(1) + 3 = 1 + 2 + 3 = 6$
For $x = 2$ :
$y = (2)^2 + 2(2) + 3 = 4 + 4 + 3 = 11$
For $x = 3$ :
$y = (3)^2 + 2(3) + 3 = 9 + 6 + 3 = 18$
For $x = 4$ :
$y = (4)^2 + 2(4) + 3 = 16 + 8 + 3 = 27$
For $x = 5$ :
$y = (5)^2 + 2(5) + 3 = 25 + 10 + 3 = 38$
Construct the table of values.
$\begin{array}{|c|c|c|c|c|c|c|c|c|} \hline x & -2 & -1 & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline y & 3 & 2 & 3 & 6 & 11 & 18 & 27 & 38 \\ \hline \end{array}$
The completed table of values is:
$\boxed{ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline x & -2 & -1 & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline y & 3 & 2 & 3 & 6 & 11 & 18 & 27 & 38 \\ \hline \end{array} }$

Point	x	y
Minimum	−1	2
y-intercept	0	3

Complete the table of values for the relation y = x2 + 2x + 3 for the range -2 x 5.

Step-by-step solution

Calculate $y$ for each $x$ value.

Construct the table of values.

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