Mathematics II Reasoning with Equations and Inequalities


Reasoning with Equations and Inequalities


Solve equations and inequalities in one variable. [Quadratics with real coefficients]
1. Solve quadratic equations in one variable. tools-icon
a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form
(x – p)2 = q that has the same solutions. Derive the quadratic formula from this form.
b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic
formula, and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives
complex solutions and write them as a ± bi for real numbers a and b.
Solve systems of equations. [Linear-quadratic systems]
7. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
For example, find the points of intersection between the line y = –3x and the circle x2 + y2 = 3.