In this lesson we’ll look at methods for factoring quadratic equations with coefficients in front of the x^2 term (that are not 1 or 0). Factoring means you’re taking the parts of an expression and rewriting it as parts that are being multiplied together (the factors). Factoring a quadratic equation means we will write equations of the form ax^2+bx+c into the form (px+r)(qx+s), where a, b, c, p, q, and s are all real numbers and a≠1,0.
Read MoreThe zeroes of a single-variable polynomial are the values of that variable at which the polynomial is equal to 0. Completing the square is a method we can use to find the zeroes of a quadratic polynomial. Another way to say this is that completing the square is a method we can use to solve the corresponding quadratic equation (the equation that has the quadratic polynomial on one side and 0 on the other side).
Read MoreWhen the discriminant is negative, the roots of the quadratic equation are complex, meaning that they’re complex numbers that include the imaginary number i. When the roots of a polynomial equation that are real numbers are also called real zeroes of the corresponding polynomial. Similarly, the roots of a polynomial equation that are complex numbers are also called complex zeroes of the corresponding polynomial.
Read MoreFactoring of quadratic polynomials (second-degree polynomials) is done by “un-FOILing,” which means we start with the result of a FOIL problem and work backwards to find the two binomial factors.
Read MoreQuadratic functions are functions in the form ax^2+bx+c=0. Integrating functions that include a quadratic can sometimes be a little difficult. There are three methods we’ll use to evaluate quadratic integrals: substitution, partial fractions, and trigonometric substitution. You should try using these techniques in the order listed above, because substitution is the easiest and fastest, and trigonometric substitution is the longest and most difficult.
Read MoreQuadratic equations create parabolas when they’re graphed, so they’re non-linear functions. There are two forms that are especially helpful when you want to know something about a parabola, which are the standard form of a parabola, and the vertex form of a parabola.
Read More
