To find the solutions to the equation x² + 2x + 3 = 0, we can use a system of equations. First, we can rewrite the quadratic equation as y = x² + 2x + 3. This represents a parabola on a graph.
Next, we introduce a horizontal line that represents the y-value we want to analyze. For example, we can graph the line y = 0 to identify where the parabola intersects this line. The points of intersection, if any, will give us the solutions to the original equation.
Thus, the system of equations to graph would be:
- y = x² + 2x + 3
- y = 0
Upon graphing these equations, you will find that the parabola does not intersect the horizontal line y = 0, indicating that there are no real solutions to the equation x² + 2x + 3 = 0. This is an example of how you can visualize the solutions to a quadratic equation using graphs.