How to Graph the Solution of y = x² + 2x

To graph the solution of the equation y = x² + 2x, follow these steps:

1. Identify the Type of Function: This is a quadratic function, which means its graph will be a parabola. The general form of a quadratic function is y = ax² + bx + c, where a, b, and c are constants. Here, a = 1, b = 2, and c = 0.
2. Find the Vertex: The vertex of the parabola can be found using the formula: x = -b/(2a). Plugging in our values, we have x = -2/(2*1) = -1. To find the y-coordinate of the vertex, substitute x = -1 back into the equation: y = (-1)² + 2(-1) = 1 – 2 = -1. Thus, the vertex is at the point (-1, -1).
3. Determine the Axis of Symmetry: The axis of symmetry for a parabola can be found using the x-coordinate of the vertex, which in this case is x = -1.
4. Create a Table of Values: Choose several x-values around the vertex to calculate corresponding y-values. For example:
   • If x = -3, then y = (-3)² + 2(-3) = 9 – 6 = 3
   • If x = -2, then y = (-2)² + 2(-2) = 4 – 4 = 0
   • If x = 0, then y = (0)² + 2(0) = 0
   • If x = 1, then y = (1)² + 2(1) = 1 + 2 = 3
5. Plot the Points: Using the points calculated from the table of values, plot the points on the graph: (-3, 3), (-2, 0), (-1, -1), (0, 0), (1, 3).
6. Draw the Parabola: Once you have plotted the points, draw a smooth curve that passes through them, making sure the curve opens upwards (since a = 1 is positive).

Now you have successfully graphed the function y = x² + 2x! The final graph should show a U-shaped curve with the vertex at (-1, -1) and symmetric about the line x = -1.