How do you plot y = x^2 + 2x + 1?

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To plot \( y = x^2 + 2x + 1 \), create a table of values and draw the corresponding points on a graph.

First, let's understand the equation \( y = x^2 + 2x + 1 \). This is a quadratic equation, which means its graph will be a parabola. The general form of a quadratic equation is \( y = ax^2 + bx + c \). In this case, \( a = 1 \), \( b = 2 \), and \( c = 1 \).

To plot the graph, start by creating a table of values. Choose a range of \( x \) values, both positive and negative, and calculate the corresponding \( y \) values. For example:

\[
\begin{array}{c|c}
x & y = x^2 + 2x + 1 \\
\hline
-3 & (-3)^2 + 2(-3) + 1 = 9 - 6 + 1 = 4 \\
-2 & (-2)^2 + 2(-2) + 1 = 4 - 4 + 1 = 1 \\
-1 & (-1)^2 + 2(-1) + 1 = 1 - 2 + 1 = 0 \\
0 & (0)^2 + 2(0) + 1 = 0 + 0 + 1 = 1 \\
1 & (1)^2 + 2(1) + 1 = 1 + 2 + 1 = 4 \\
2 & (2)^2 + 2(2) + 1 = 4 + 4 + 1 = 9 \\
\end{array}
\]

Next, plot these points on a graph with \( x \)-axis and \( y \)-axis. The points you have are (-3, 4), (-2, 1), (-1, 0), (0, 1), (1, 4), and (2, 9).

After plotting these points, draw a smooth curve through them. You will see that the graph forms a U-shaped parabola opening upwards. The vertex of the parabola, which is the lowest point, is at (-1, 0). This is because the equation can be rewritten as \( y = (x + 1)^