Quadratic Formula Explainer with Simple Graph Animations

The quadratic formula starts with the standard form of a quadratic equation.Let's understand what each letter represents in this standard form.Now, let's look at the quadratic formula itself.Let's break down each part of this formula to understand its components.Let's look at a specific example to identify these components.In this equation, x squared plus five x plus six equals zero, we can identify each component.Let's summarize what we've learned about these components.Now that we understand the components, we're ready to solve quadratic equations.Now let's solve this quadratic equation step by step.We'll substitute our values into the quadratic formula: a equals 1, b equals 5, and c equals 6.Let's start by calculating what's under the square root. Five squared is twenty-five.Twenty-five minus twenty-four equals one.The square root of one is simply one.Now we'll calculate both the plus and minus versions separately.For the plus version, negative five plus one equals negative four.Negative four divided by two gives us negative two.For the minus version, negative five minus one equals negative six.Negative six divided by two gives us negative three.So our equation has two solutions: x equals negative two and x equals negative three.Now let's visualize our quadratic equation on a coordinate plane.Here's the graph of y equals x squared plus five x plus six.The x-intercepts are the points where our parabola crosses the x-axis. These are our solutions: x equals negative two and x equals negative three.Let's verify these solutions by plugging them back into our original equation.For x equals negative two: When we square negative two, add five times negative two, and add six...We get zero, confirming this is a solution.Similarly for x equals negative three: We square negative three, add five times negative three, and add six...Again, we get zero, verifying our second solution.Watch as we trace along the parabola. Notice how the y-value becomes zero exactly at our solution points.Let's summarize what we've learned about verifying quadratic solutions.Thanks for learning about quadratic equations with Spark.E!