Quadratic Formula Explainer with Simple Graph Animations

Starting with our quadratic equation x squared plus 5x plus 6 equals zeroWe'll use the quadratic formula to solve for xFirst, let's identify our values: a is 1, b is 5, and c is 6Now, let's substitute these values into the quadratic formulaUnder the square root, we first calculate 5 squared, which is 25, minus 4 times 1 times 6, which is 24This simplifies to the square root of 1The square root of 1 is simply 1Now we'll calculate both solutions. First, using the plus signAnd then using the minus signLet's verify these solutions by plugging them back into our original equationWhen we substitute x equals negative 2And when we substitute x equals negative 3Now that we've found our solutions algebraically, let's see what they look like on a graphNow let's verify our solutions graphically by plotting the parabola.Our quadratic equation y equals x squared plus five x plus six can be graphed as a parabola.The solutions we found, x equals negative two and x equals negative three, are the x-intercepts of this parabola.These points represent where the parabola crosses the x-axis, meaning where y equals zero.Let's verify these solutions by plugging them back into our original equation.The parabola's axis of symmetry passes through its vertex at x equals negative two point five, confirming that our two solutions are equidistant from this line.The upward-facing parabola confirms that these are the only two solutions, as it only crosses the x-axis at these two points.