Quadratic Formula Explainer with Simple Graph Animations

The quadratic formula helps us solve quadratic equations that are in standard form.Here's the complete quadratic formula. It may look intimidating, but we'll break it down piece by piece.In the standard form, we have three important components.The coefficient 'a' is the number in front of x squared.The coefficient 'b' is the number in front of x.And 'c' is the constant term with no variable.Let's look at a specific example: x squared plus five x plus six equals zero.In this equation, a equals one, b equals five, and c equals six.These values will be plugged into the quadratic formula. The negative b term goes on top, followed by plus or minus the square root term, all divided by two a.Now let's solve our equation by substituting the values into the quadratic formula.We substitute b equals 5, a equals 1, and c equals 6 into the formula.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 under the square root.The square root of one is simply one, giving us negative five plus or minus one, over two.Now let's solve both the plus and minus cases separately.For the plus case, negative five plus one is negative four, divided by two equals negative two.For the minus case, negative five minus one is negative six, divided by two equals negative three.Therefore, our equation has two solutions: x equals negative two and x equals negative three.Now let's verify our solutions graphically by plotting the parabola.Here's our parabola y equals x squared plus five x plus six.The x-intercepts are the points where the parabola crosses the x-axis, where y equals zero.Let's verify that x equals negative two is a solution by plugging it back into our equation.Similarly, let's verify that x equals negative three is also a solution.Let's summarize what we've learned about solving quadratic equations.The x-intercepts of our parabola are the solutions to our quadratic equation.We've verified that both x equals negative two and x equals negative three give us y equals zero.And our graph provides visual confirmation of our algebraic solution.Thanks for learning about quadratic equations with Spark.E!