How does quadratic equation work

This means that there must then be two x -intercepts on 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. In general, no, you really shouldn't. The "solution" or "roots" or "zeroes" of a quadratic are usually required to be in the "exact" form of the answer.

You can use the rounded form when graphing if necessary , but "the answer s " from the Quadratic Formula should be written out in the often messy "exact" form. In the example above, the exact form is the one with the square roots of ten in it.

If you're wanting to graph the x -intercepts or needing to simplify the final answer in a word problem to be of a practical "real world" form, then you can use the calculator's approximation. 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. Page 1 Page 2 Page 3. All right reserved. Web Design by.

Skip to main content. Purplemath When would I use the Quadratic Formula? Content Continues Below. What is the Quadratic Formula? A quadratic equation with real numbers as coefficients can have the following:.

Two different real roots if the discriminant b 2 — 4 ac is a positive number. Setting all terms equal to 0,. Then substitute 1 which is understood to be in front of the x 2 , —5, and 6 for a , b , and c, respectively, in the quadratic formula and simplify. Because the discriminant b 2 — 4 ac is positive, you get two different real roots. Example produces rational roots.

In Example , the quadratic formula is used to solve an equation whose roots are not rational. Then substitute 1, 2, and —2 for a , b , and c, respectively, in the quadratic formula and simplify. Since the discriminant b 2 — 4 ac is 0, the equation has one root. The quadratic formula can also be used to solve quadratic equations whose roots are imaginary numbers, that is, they have no solution in the real number system.

Since the discriminant b 2 — 4 ac is negative, this equation has no solution in the real number system. But if you were to express the solution using imaginary numbers, the solutions would be. A third method of solving quadratic equations that works with both real and imaginary roots is called completing the square.

Using the value of b from this new equation, add to both sides of the equation to form a perfect square on the left side of the equation. Add or to both sides. There is no solution in the real number system. Previous Quiz Solving Quadratic Equations. Next Word Problems.