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Make a table of solutions for the equation
y=x^(2)+3. Then, choose the correct graph for the equation.

Make a table of solutions for the equation $y=x^{2}+3$ . Then, choose the correct graph for the equation.

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Find the vertex of the transformed function

Full solution

Q. Make a table of solutions for the equation

y=x^{2}+3

. Then, choose the correct graph for the equation.

Identify Equation and Plan: Identify the equation and plan to create a table of values. $\newline$ Equation: $y = x^2 + 3$ . $\newline$ Choose values for $x$ : $-2$ , $-1$ , $0$ , $1$ , $2$ .
Calculate $y$ for $x = -2$ : Calculate $y$ for $x = -2$ . $\newline$ $y = (-2)^2 + 3 = 4 + 3 = 7$ . $\newline$ Table so far: $(-2, 7)$ .
Calculate $y$ for $x = -1$ : Calculate $y$ for $x = -1$ . $\newline$ $y = (-1)^2 + 3 = 1 + 3 = 4.$ $\newline$ Table so far: $(-2, 7$ ), $(-1, 4$ ).
Calculate $y$ for $x = 0$ : Calculate $y$ for $x = 0$ . $\newline$ $y = (0)^2 + 3 = 0 + 3 = 3$ . $\newline$ Table so far: $(-2, 7$ ), $(-1, 4$ ), $(0, 3)$ .
Calculate $y$ for $x = 1$ : Calculate $y$ for $x = 1$ . $\newline$ $y = (1)^2 + 3 = 1 + 3 = 4$ . $\newline$ Table so far: $(-2, 7)$ , $(-1, 4)$ , $(0, 3)$ , $(1, 4)$ .
Calculate $y$ for $x = 2$ : Calculate $y$ for $x = 2$ . $\newline$ $y = (2)^2 + 3 = 4 + 3 = 7.$ $\newline$ Table so far: $(-2, 7)$ , $(-1, 4)$ , $(0, 3)$ , $(1, 4)$ , $(2, 7)$ .
Review Table and Choose Graph: Review the table and choose the correct graph. $\newline$ Table: $(-2, 7)$ , $(-1, 4)$ , $(0, 3)$ , $(1, 4)$ , $(2, 7)$ . $\newline$ Graph should be a parabola opening upwards with vertex at $(0, 3)$ .

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