Quadratic formula

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The "solutions" of an equation are also the x-intercepts of the corresponding graph. This is always true. The standard quadratic formula is a lot to remember: It's a maze of numbers, letters, and square roots. Page 1. Warning: The "solution" or "roots" or "zeroes" of a quadratic are usually required to be in the "exact" form of the answer. Remember that "b2" means "the square of ALL of b, including its sign", so don't leave b2 being negative, even if b is negative, because the square of a negative is a positive. Discriminant Disc. But that offset makes us do extra work. Step 3: Complete The Square The trick to canceling the offset is completing the square. But sometimes the quadratic is too messy, or it doesn't factor at all, or you just don't feel like factoring.

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. Page 1.

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Completing the square and solving gives us: Pretty clean! This is always true.

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Let's solve this equation: My thought process: first, divide everything by 3. Remember that "b2" means "the square of ALL of b, including its sign", so don't leave b2 being negative, even if b is negative, because the square of a negative is a positive.

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And it's a "2a" under there, not just a plain "2". 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.

How would my solution look in the Quadratic Formula? I will apply the Quadratic Formula.

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In other words, don't be sloppy and don't try to take shortcuts, because it will only hurt you in the long run. While factoring may not always be successful, the Quadratic Formula can always find the solution. This is always true. It's a I will apply the Quadratic Formula. 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. Discriminant Disc. Step 3: Complete The Square The trick to canceling the offset is completing the square.

Using the radius formula, we get: Pretty fast, right? No need to leave things sitting around. The "solutions" of an equation are also the x-intercepts of the corresponding graph.

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Intuition for the Quadratic Formula