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The Quadratic Formula is an essential tool you'll remember long after high school, enabling you to solve any quadratic equation. This guide walks you through the step-by-step process of completing the square, from isolating the variable to extracting the square root. By the end, you'll be equipped to find the roots of quadratic equations and the zeros of quadratic functions efficiently. Whether you're reviewing for exams or refreshing your knowledge, mastering this formula is crucial for your mathematical toolkit.
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The Quadratic Formula Something you will remember long after you have left high school and not know why!
The Quadratic Formula • Start with following quadratic equation: • 0 • Let’s try to solve it by completing the square, since there doesn’t seem to be anything else we can do.
The Quadratic Formula • Take of the factor “a” from the first two terms • Now, take the coefficient of the “x” term, divide it by two, then square it, add and subtract it.
The Quadratic Formula • Factor the first three terms of the R.S. Simplifying this equation, you get
The Quadratic Formula • Move what you can easily to the L.S. • Now it gets really interesting! • Take the square root on both sides
The Quadratic Formula • = • OK, so now we need to get “x” completely by itself • Like that!
The Quadratic Formula • Now let’s clean it up a bit • Almost there
The Quadratic Formula • Finally we have it, the quadratic formula! • We can now use this to solve problems. i.e. find the roots of quadratic equations or the zeros of quadratic functions.
