# What are a b and c in the quadratic formula May 21,  · One of the most important skills an algebra student learns is the quadratic formula, or x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a}. With the quadratic formula, solving any quadratic equation of the form ax^{2} + bx + c = 0 becomes a simple. Worked example: quadratic formula (negative coefficients) Using the quadratic formula: number of solutions. Up Next. Using the quadratic formula: number of solutions. Our mission is to provide a free, world-class education to anyone, anywhere. Khan Academy is a (c)(3) nonprofit organization. Donate or volunteer today! Site Navigation. About.

Example 2 — Solve:. Example 3 — Solve:. Example 4 — Solve:. Example 5 — Solve:. Step 1 : Identify what type of underlayment for tile floor, b, and c and plug them into the quadratic formula. Step 2 : Use the order of operations to simplify the quadratic formula. Step 3 : Simplify the radical, if you can. In this case you can simply the radical into:. Step 4 : Reduce the problem, if you can.

In this case you can reduce the entire problem by 2. Step 1 : To use the quadratic formula, the equation must be equal to zero, so move the —5 back to the left hand side. Step 2 : Identify a, b, and c and plug them into the quadratic formula. Step 3 : Use the order of operations to simplify the quadratic formula.

Step 4 : Simplify the radical, if you can. Step 5 : Reduce the problem, if you can. Step 1 : To use the quadratic formula, the equation must be equal to zero, so move the 7x and 6 back to the left hand side. In this case you can not simply the radical.

In this case you can not reduce the problem. Step 1 : To use the quadratic formula, the equation must be equal to zero, so move the —4x back to the left hand side. In this case you can simply the radical and remember that the square root of a negative number results in an imaginary number, so you should get:. Step 6 : Reduce the problem, if you can. Step 1 : To use the quadratic formula, the equation must be equal to zero, so move the 8 back to the left hand side.

Step 5 : Since this problem does not contain any square roots, you can simplify the final answer into:.

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The quadratic formula helps us solve any quadratic equation. First, we bring the equation to the form ax²+bx+c=0, where a, b, and c are coefficients. Then, we plug these coefficients in the formula: (-b±√(b²-4ac))/(2a). See examples of using the formula to solve a variety of equations. This page will show you how to use the quadratic formula to get the two roots of a quadratic equation. Fill in the boxes to the right, then click the button to see how it’s done. It is most commonly note that a is the coefficient of the x 2 term, b is the coefficient of the x term, and c is the constant term (the term that doesn’t have and. About the Quadratic Formula Plus/Minus. First of all what is that plus/minus thing that looks like ±? The ± means there are TWO answers: x = −b + √(b 2 − 4ac) 2a. x = −b − √(b 2 − 4ac) 2a. Here is an example with two answers: But it does not always work out like that! Imagine if the curve "just touches" the x-axis.

Quadratic Formula Discriminant Disc. But sometimes the quadratic is too messy, or it doesn't factor at all, or you just don't feel like factoring. While factoring may not always be successful, the Quadratic Formula can always find the solution. Practice The Quadratic Formula. The Quadratic Formula is derived from the process of completing the square, and is formally stated as:.

Also, the " 2 a " in the denominator of the Formula is underneath everything above, not just the square root. And it's a " 2 a " under there, not just a plain " 2 ". Remember that " b 2 " means "the square of ALL of b , including its sign", so don't leave b 2 being negative, even if b is negative, because the square of a negative is a positive. In other words, don't be sloppy and don't try to take shortcuts, because it will only hurt you in the long run. Trust me on this!

How would my solution look in the Quadratic Formula? The corresponding x -values are the x -intercepts of the graph. Graphing, we get the curve below:. This can be useful if you have a graphing calculator, because you can use the Quadratic Formula when necessary to solve a quadratic, and then use your graphing calculator to make sure that the displayed x -intercepts have the same decimal values as do the solutions provided by the Quadratic Formula. Note, however, that the calculator's display of the graph will probably have some pixel-related round-off error, so you'd be checking to see that the computed and graphed values were reasonably close; don't expect an exact match.

I will apply the Quadratic Formula. Warning: The "solution" or "roots" or "zeroes" of a quadratic are usually required to be in the "exact" form of the answer. In the example above, the exact form is the one with the square roots of ten in it. You'll need to get a calculator approximation in order to graph the x-intercepts or to simplify the final answer in a word problem. But unless you have a good reason to think that the answer is supposed to be a rounded answer, always go with the exact form.

Just as in the previous example, the x -intercepts match the zeroes from the Quadratic Formula. This is always true. The "solutions" of an equation are also the x -intercepts of the corresponding graph.

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