How to Graph a Quadratic Equation
This video shows three examples of solutions of a quadratic equation on a graph. When there is a parabola that crosses the x axis two times, each intersect will be a solution. When there is a parabola that intersects the x axis only once, there is only one solution, which is where the vertex touches the x axis. When the parabola does not touch the x axis, there are no real solutions, or there are two complex solutions.
Solutions of a Quadratic Equation on a Graph
The first graph we have here is a parabola which crosses the x axis two times. Which means there are two solutions to this equation y equals x squared, plus x, minus 6. Those two solutions are the places where the parabola crosses the x axis.
This one has two solutions. Those two solutions are positive 2 and -3, x equals -3 and positive 2. Those are the two solutions. However, the parabola won’t always cross the x axis two times. Sometimes it may only intersect it one time.
When that happens it’s the vertex that touches the x axis one time. This intersection, this parabola, this graph, would only have one solution. The solution here is the vertex where it intersects the x axis at positive 3. Here solution would just be x equals 3.
The third situation is when the parabola never touches the x axis. That would be when you have two complex solutions, or no real solutions. Again, those two complex solutions because it never actually touches the x axis, so there aren’t any real solutions to the quadratic equation.
Here are three different situations, you can have two solutions to your equation, one solution, or none at all. You can tell what those solutions are just by looking at the graph of the parabola for the quadratic equation. You can see if it crosses twice, and those would be your two solutions.
If it only intersects your x axis one time, and that your one solution. Or if it never touches the x axis at all, and that means that the solutions are complex and they are not real.