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Remedial Algebra I25 chapters | 248 lessons | 1 flashcard set

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Watch this video lesson to learn how you can use the quadratic formula to solve certain types of problems. Learn what kinds of equations you can solve using this formula as well as how easy it is to use this formula.

The **quadratic formula** (*x* = (-b +/- sqrt (b^2 - 4ac)) / (2a)) is a famous formula that allows you to solve any type of quadratic equation. A quadratic equation is a second degree polynomial, which means that its highest exponent is 2. An example of a quadratic equation is *x*^2 + 3*x* + 4 = 0. You can see that the highest exponent is 2. The usefulness of the quadratic formula is seen when we have a quadratic equation that can't be solved by other methods. When other methods fail, the quadratic formula succeeds. Do your best to remember this formula.

In order to use the quadratic formula, the quadratic equation must be in standard form. What does this mean? It means that your equation must be written in decreasing order, starting with the term with the largest exponent and then going down based on the exponent. So, your quadratic equation written in standard form will look like this: a*x*^2 + b*x* + c = 0 where a, b and c are your values.

Do you see how these letters are also used in the quadratic formula? Yes, when you write your quadratic equation in standard form, you can easily spot which value is your a value, your b value and your c value. Once you have all three of these values labeled, you can plug these values into your quadratic formula to solve your equation. If you see a missing term, then the letter for that term will be 0.

Let's try an example. Say we have the quadratic 2*x*^2 + 3*x* + 1 = 0 that we want to solve. We see that the equation is already written in standard form, so we can go ahead and label our a, b and c. We compare this to the standard form and we find that our a value is 2, our b value is 3 and our c value is 1. Plugging these into our quadratic formula gives us *x* = (-3 +/- sqrt (3^2 - (4 * 2 * 1))) / (2 * 2).

Once we have plugged in our values, we can now evaluate our formula to find our answer. The formula doesn't look nearly as bad now, does it? With all these numbers in place, it now looks manageable. Let's go ahead and evaluate to see what we get. We first tackle the inside part of the square root. We square the three to get 9. Then we multiply 4 * 2 * 1 = 8. Now we subtract the 8 from the 9 to get 1. Now we deal with the denominator by multiplying 2 * 2 = 4.

So, now our quadratic formula looks like *x* = (-3 +/- sqrt (1)) / 4. We see that there is a +/-. That tells us that we now need to split our formula into two separate formulas, one for the plus part and another for the minus part. That tells us that we will have two possible answers. We have:

*x*= (-3 + sqrt (1)) / 4*x*= (-3 - sqrt (1)) / 4

Evaluating the first, we get *x* = (-3 + sqrt (1)) / 4 = (-3 + 1) / 4, which equals -2/4, which equals -1/2. So -1/2, or -0.5, is the first part of our answer. The second part is *x* = (-3 - sqrt (1)) / 4 = (-3 - 1) / 4, which equals -4/4 = -1. So, our two answers are -0.5 and -1. We are done!

One thing to note here is that if the square root part is negative, then we can stop right there. Why is this? When we have a negative square root, we will get an error when we use a calculator to calculate it, so that tells us that we are dealing with numbers that aren't real. Because of this, we can stop and say that there are no real solutions.

Let's recap. We've learned that the **quadratic formula** is this: *x* = (-b +/- sqrt (b^2 - 4ac)) / (2a) and can be used to solve any quadratic equation. To use the formula, our quadratic equation must be in the standard form of a*x*^2 + b*x* + c = 0. Once our equation is in standard form, we compare our problem with the standard form to find our a, b and c values. Once we have our values, we plug them into our formula, and then evaluate to get our answer. If the part under the square root is negative, though, we stop and say that there are no real answers.

Once you have completed this lesson you should be able to identify and solve a quadratic equation using the quadratic formula.

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Remedial Algebra I25 chapters | 248 lessons | 1 flashcard set

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