If you are looking at a graph of a quadratic equation, how do you determine where the solutions are?
To determine the solutions of a quadratic equation by looking at its graph, you need to identify the x-values where the graph intersects the x-axis. These x-values represent the solutions or roots of the quadratic equation.
Follow these steps to determine the solutions visually:
1. Examine the x-axis: On the graph, locate the x-axis or horizontal line. The x-axis represents all possible values of x.
2. Look for intersecting points: Observe where the graph of the quadratic equation intersects or touches the x-axis. These points are called the x-intercepts or zeros of the equation.
3. Identify the x-values: The x-values where the graph intersects the x-axis are the solutions or roots of the quadratic equation. Each intercept corresponds to one solution.
Remember that a quadratic equation can have zero, one, or two solutions, depending on the nature of the graph. If the graph does not intersect the x-axis at any point, it means the equation has no real solutions. If the graph touches the x-axis at only one point, the equation has one real solution. And if the graph intersects the x-axis at two distinct points, the equation has two real solutions.