Georgia HomeroomAA.FGR.5Polynomials & Complex Solutions
Extend exploration of quadratic solutions to include real and non-real numbers and explore how these numbers behave under familiar operations and within real-world situations; create polynomial expressions, solve polynomial equations, graph polynomial functions, and model real-world phenomena.
Appears in: Mathematics, High School
Expectations
AA.FGR.5.1Graph and analyze quadratic functions in contextual situations and include analysis of data sets with regressions.
AA.FGR.5.2Define complex numbers $i$ such that $i^2 = –1$ and show that every complex number has the form $a + bi$ where $a$ and $b$ are real numbers and that the complex conjugate is $a - bi$.
AA.FGR.5.3Use the relation $i^2 = –1$ and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
AA.FGR.5.4Use the structure of an expression to factor quadratics.
AA.FGR.5.5Write and solve quadratic equations and inequalities with real coefficients and use the solution to explain a mathematical, applicable situation.
AA.FGR.5.6Solve systems of quadratic and linear functions to determine points of intersection.
AA.FGR.5.7Create and analyze quadratic equations to represent relationships between quantities as a model for contextual situations.
AA.FGR.5.8Identify the number of zeros that exist for any polynomial based upon the greatest degree of the polynomial and the end behavior of the polynomial by observing the sign of the leading coefficient.
AA.FGR.5.9Identify zeros of polynomial functions using technology or pre-factored polynomials and use the zeros to construct a graph of the function defined by the polynomial function. Analyze identify key features of these polynomial functions.
AA.FGR.5.10Use the structure of an expression to factor polynomials, including the sum of cubes, the difference of cubes, and higher-order polynomials that may be expressed as a quadratic within a quadratic.
AA.FGR.5.11Using all the zeros of a polynomial function, list all the factors and multiply to write a multiple of the polynomial function in standard form.
Georgia Milestones coverage
No Georgia Milestones blueprint cites this standard.