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Important Information About Solutions of Quadratic Equations

I am completely lost in this class. I really want to understand the concepts in this chapter. Can anyone help?

(1) How do you know if a quadratic equation will have one, two, or no solutions?

(2) How do you find a quadratic equation if you are only given the solution?

(3) Is it possible to have different quadratic equations with the same solution? Explain.

(4) Provide quadratic equations examples with one or two solutions with which they must create a quadratic equation.

Solution Preview

First off ... a quadratic equation is a polynomial that has an x^2 term (an x-squared term) but doesn't have an x^3, x^4, x^5 term or anything larger. A polynomial is an equation with whole number exponents for the x's. It is a "normal looking" equation -- it doesn't have anything that looks like a square root and doesn't have any x's on the bottom of fractions.

If you graph a quadratic equation, it looks like a parabola. It opens up if the x^2 is multiplied by a positive number and opens down if it's multiplied by a negative number.

A solution to the quadratic equation is a number(s) so that if you make x equal that number (or numbers), y equals 0. You can also think of it as the point where the parabola crosses the x-axis.

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Solution Summary

The solution defines the terms "quadratic equation", "polynomial", and "solution". It then answers all four questions using examples to clarify the concepts.