How do you solve a quadratic equation using the formula?

Solving a quadratic equation means finding the values of x that make ax squared plus bx plus c equal to zero, and you can do this using the quadratic formula x equals negative b plus or minus the square root of b squared minus four a c all over two a.

Think of a quadratic like a hill or a valley drawn by a curved line; the places where that curve touches the horizontal line are the solutions for x. The quadratic formula works every time: first compute b squared minus four a c, which tells you whether the curve crosses the line twice, just touches it, or misses it; then take the square root of that number, add and subtract it from negative b, and divide both answers by two a. If b squared minus four a c is positive you get two different numbers, if it is zero you get one number twice, and if it is negative there are no real number answers. Always simplify by dividing every term by the greatest common factor first if possible, and keep track of signs when you plug numbers into the formula.

Students often forget to calculate b squared correctly and make sign errors, so double check that you square the entire b term and keep the minus sign outside the squared value; another common mistake is dividing by two a without computing two times a first, so perform multiplication before division to avoid sloppy fractions, and a third is mishandling a negative discriminant by expecting a real answer when there is none, so check the value under the square root and state clearly when no real solutions exist.

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Solving Quadratics with the Formula

1. Compute b squared minus four a c
2. Take the square root of discriminant
3. Add and subtract from negative b
4. Divide results by two a
5. Simplify by greatest common factor
6. Keep track of signs when plugging numbers

Common Quadratic Mistakes and Fixes

1. Miscomputing b squared and sign errors
2. Forgetting to multiply two times a
3. Mishandling negative discriminant expecting real answers

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