Quadratic Formula Explainer with Simple Graph Animations

Now let's solve x squared plus 5x plus 6 equals 0 step by step.We'll substitute our values a equals 1, b equals 5, and c equals 6 into the quadratic formula.Let's simplify what's under the square root first. Five squared is twenty-five, and four times a times c is twenty-four.Twenty-five minus twenty-four equals one.The square root of one is simply one.Now let's solve for both the positive and negative cases. First, when we add one to negative five.And when we subtract one from negative five.Therefore, our solutions are x equals negative two and x equals negative three.Now that we've found our solutions algebraically, let's see what they mean graphically.The quadratic equation forms a parabola when graphed. For our equation x squared plus 5x plus 6, this is what it looks like.The solutions we found, negative three and negative two, are the x-intercepts - the points where the parabola crosses the x-axis.At these points, y equals zero, which is why they're called x-intercepts.The discriminant we calculated earlier determines how many times the parabola crosses the x-axis.In our case, we got two solutions because the discriminant was positive, giving us two x-intercepts.When the discriminant equals zero, the parabola touches the x-axis at exactly one point.And when the discriminant is negative, the parabola never crosses the x-axis, meaning there are no real solutions.Let's return to our original equation, where we can clearly see both solutions on the graph.