Quadratics & Other Nonlinear Functions - Reporting Category 5
Quadratic and other nonlinear functions. The student understands that the graphs of quadratic functions are affected by the parameters of the function and can interpret and describe the effects of changes in the parameters of quadratic functions. The student understands there is more than one way to solve a quadratic equation and solves them using appropriate methods. The student understands there are situations modeled by functions that are neither linear nor quadratic and models the situations.
(A.9) Quadratic and other nonlinear functions. The student understands that the graphs of quadratic functions are affected by the parameters of the function and can interpret and describe the effects of changes in the parameters of quadratic functions. The student is expected to
(A) determine the domain and range for quadratic functions in given situations; Supporting Standard
(B) investigate, describe, and predict the effects of changes in a on the graph of y = ax2 + c; Supporting Standard
(C) investigate, describe, and predict the effects of changes in c on the graph of y = ax2 + c; and Supporting Standard
(D) analyze graphs of quadratic functions and draw conclusions. Readiness Standard
(A.10) Quadratic and other nonlinear functions. The student understands there is more than one way to solve a quadratic equation and solves them using appropriate methods. The student is expected to
(A) solve quadratic equations using [concrete] models, tables, graphs, and algebraic methods; and Readiness Standard
- Solve a quadratic equation using square roots (Algebra 1 - BB.4)
- Solve an equation using the zero product property (Algebra 1 - BB.5)
- Solve a quadratic equation by factoring (Algebra 1 - BB.6)
- Complete the square (Algebra 1 - BB.7)
- Solve a quadratic equation by completing the square (Algebra 1 - BB.8)
- Solve a quadratic equation using the quadratic formula (Algebra 1 - BB.9)
- Using the discriminant (Algebra 1 - BB.10)
(B) make connections among the solutions (roots) of quadratic equations, the zeros of their related functions, and the horizontal intercepts (x-intercepts) of the graph of the function. Supporting Standard
- Characteristics of quadratic functions (Algebra 1 - BB.1)
- Solve a quadratic equation using square roots (Algebra 1 - BB.4)
- Solve an equation using the zero product property (Algebra 1 - BB.5)
- Solve a quadratic equation by factoring (Algebra 1 - BB.6)
(A.11) Quadratic and other nonlinear functions. The student understands there are situations modeled by functions that are neither linear nor quadratic and models the situations. The student is expected to
(A) use patterns to generate the laws of exponents and apply them in problem-solving situations; Supporting Standard
- Multiplication with exponents (Algebra 1 - V.4)
- Division with exponents (Algebra 1 - V.5)
- Multiplication and division with exponents (Algebra 1 - V.6)
- Power rule (Algebra 1 - V.7)
- Simplify expressions involving exponents (Algebra 1 - V.8)
(B) analyze data and represent situations involving inverse variation using [concrete] models, tables, graphs, or algebraic methods; and Supporting Standard
- Identify direct variation and inverse variation (Algebra 1 - R.6)
- Write inverse variation equations (Algebra 1 - R.7)
- Write and solve inverse variation equations (Algebra 1 - R.8)
(C) analyze data and represent situations involving exponential growth and decay using [concrete] models, tables, graphs, or algebraic methods. Supporting Standard
