One of the most common formulas used in introductory algebra courses is the quadratic formula, which is (-b +/- sqrt([b^2] - 4ac))/2a. It is used to solve quadratic equations that are written in the form of ax2 + bx + c = 0.
Other commonly used formulas in algebra are known as the laws of exponents and are used to solve equations that include variables taken to an exponential power. For example, the problem (x^a)(x^b) is equal to x^(a + b). Similarly, (x^a)^b is equal to x^ab.
When two different variables are multiplied and taken to the same power, the equation is solved using the formula where (xy)^a = (x^a)(y^a). Another common formula is used to find the square of a binomial expression. For example, the expression (x + y)^2 is solved by using the formula (x^2) + 2xy + (y^2).
Solving problems on an xy-axis may use the algebraic formulas for different shapes. These include the formula (x^2) + (y^2) = (r^2) for a circle, (x^2)/(a^2) + (y^2)/(b^2) = 1 for an ellipse and 4py = (x^2) for a parabola. Also for graphs, the formula y = mx + b is known as the point-slope formula. The formula for the slope is the rise over the run.