(Limit to linear equations and quadratic functions.) Understand that such systems may have zero, one, two, or infinitely many solutions. A2.AREI.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.Recognize when the quadratic formula gives complex solutions and write them as a + b for real numbers a and b. A2.AREI.4.b Solve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation.
Interpret the solution within the context of the situation. Solve such systems using graphical and analytical methods, including linear programing.
A2.ACE.3 Use systems of equations and inequalities to represent constraints arising in real-world situations.Graph the equations on coordinate axes using appropriate labels, units, and scales. A2.ACE.2 Create equations in two or more variables to represent relationships between quantities.Interpret the solutions and determine whether they are reasonable. A2.ACE.1 Create and solve equations and inequalities in one variable that model real-world problems involving linear, quadratic, simple rational, and exponential relationships.(Limit to polynomials with degrees 3 or less.) Write a polynomial function of least degree corresponding to a given graph. A2.AAPR.3 Graph polynomials identifying zeros when suitable factorizations are available and indicating end behavior.A2.AAPR.1 Add, subtract, and multiply polynomials and understand that polynomials are closed under these operations.A2.AAPR Arithmetic with Polynomials and Rational Expressions.
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