Quadratic Formula Made Easy with Animations

The quadratic formula helps us solve quadratic equations that are in standard form.A quadratic equation in standard form always has three key components: a term with x squared, a term with x, and a constant term.The coefficient 'a' goes with x squaredThe coefficient 'b' goes with xAnd 'c' is our constant termTo solve any quadratic equation, we can use the quadratic formula.Notice how a, b, and c appear in different places throughout the formula.Let's look at a specific example: two x squared plus five x minus three equals zero.In this equation, a equals twob equals fiveand c equals negative threeThese are the values we'll use in the quadratic formula to solve this equation.Let's solve x squared plus 6x plus 5 equals 0 using the quadratic formula.First, we identify our values: a equals 1, b equals 6, and c equals 5.Let's start by calculating negative b. Since b is 6, negative b is negative 6.Next, we calculate b squared, which is 6 squared, giving us 36.For 4ac, we multiply 4 times 1 times 5, giving us 20.Under the square root, we subtract 4ac from b squared: 36 minus 20 equals 16.The square root of 16 is 4.Now comes the important part: the plus or minus symbol means we need to solve this two ways.When we add 4, we get negative 6 plus 4, which is negative 2, divided by 2, giving us negative 1.When we subtract 4, we get negative 6 minus 4, which is negative 10, divided by 2, giving us negative 5.Now let's complete our solution by simplifying the square root.First, we calculate that thirty-six minus twenty equals sixteen under the square root.The square root of sixteen is four.Now we handle the plus-minus symbol by splitting into two equations.For the plus case, negative six plus four equals negative two, divided by two gives us negative one.For the minus case, negative six minus four equals negative ten, divided by two gives us negative five.Let's visualize these solutions on a graph. The parabola represents our quadratic equation x squared plus six x plus five equals zero.The x-intercepts occur at x equals negative five and x equals negative one, exactly matching our solutions.Let's verify these solutions by plugging them back into the original equation.For x equals negative five, let's substitute and simplify.Similarly for x equals negative one, we can verify it also works.Let's review what we've learned about solving quadratic equations.The plus-minus symbol gives us two solutions, which appear as x-intercepts on our parabola. And we should always verify our answers by plugging them back into the original equation.Thanks for learning about quadratic equations with Spark.E!