Quadratic Formula Explainer with Simple Graph Animations

Now that we have our equation x squared plus five x plus six equals zero, let's solve it step by step.First, we'll substitute our values: negative five, plus or minus the square root of five squared minus four times one times six, all over two times one.Let's simplify what's under the square root. Five squared is twenty-five, and four times one times six is twenty-four.Twenty-five minus twenty-four equals one, so we have the square root of one.The square root of one is simply one, giving us negative five plus or minus one, over two.The plus or minus symbol means we need to solve this two ways: one with plus one, and one with minus one.For the first equation, negative five plus one equals negative four, divided by two equals negative two.For the second equation, negative five minus one equals negative six, divided by two equals negative three.Therefore, our equation has two solutions: x equals negative two or x equals negative three.Now let's visualize our quadratic equation and verify our solutions graphically.Here's the graph of our quadratic function x squared plus 5x plus 6.Remember, we found two solutions: x equals negative 6 and x equals negative 4.These solutions are the x-intercepts of our parabola, where the graph crosses the x-axis.As we move this horizontal line up and down, notice how it intersects the parabola at exactly two points when y equals zero.Let's verify that negative 6 is indeed a solution by plugging it back into our original equation.Similarly, let's verify that negative 4 is also a solution.Let's review what we've learned about quadratic equations and their graphs.Thanks for learning about quadratic equations with Spark.E!