Quadratic Formula Explainer with Simple Graph Animations

Now let's substitute our values into the quadratic formula.We'll plug in a equals 1, b equals 5, and c equals 6.First, let's simplify what's inside 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 can split this into two solutions using the plus or minus symbol.For the positive case, negative five plus one, divided by two, equals negative two.For the negative case, negative five minus one, divided by two, equals negative three.These are our two solutions to the quadratic equation x squared plus five x plus six.Now let's visualize our quadratic equation on a coordinate plane.Here's our quadratic function: f of x equals x squared plus five x plus six.As we draw the parabola, notice how it opens upward because the coefficient of x squared is positive.The x-intercepts are the points where the parabola crosses the x-axis. These are our solutions from the quadratic formula.The parabola is symmetric around its vertex, which occurs at x equals negative two point five.Let's verify that negative two is indeed a solution by plugging it back into our original equation.Similarly, let's verify that negative three is also a solution.Notice that the y-intercept is at six, which is our constant term in the quadratic equation.The graphical representation shows us that this parabola has exactly two real solutions, matching our algebraic calculations.