Solve quadratic equations by inspection (e.g., for x² = 49), taking square This standard is related to HS.N-CN.7. (ND) roots, completing the square, the quadratic formula and factoring, as It is appropriate for all students to be able to recognize when the ↑Comment: appropriate to the initial form of the equation. Recognize when the quadratic quadratic formula gives complex solutions. The pre-requisite for this standard is the formula gives complex solutions and write them as a ± bi for real numbers a and b. understanding of complex numbers and their properties. (ND) Cluster: Solve systems of equations. Code Standards Annotation Prove that, given a system of two equations in two variables, replacing one Students might by providing a formal proof, demonstrating, or justifying. “prove” equation by the sum of that equation and a multiple of the other produces a system See the glossary for a definition of proof.” (ND) “mathematical with the same solutions. Solve systems of linear equations exactly and approximately (e.g., with graphs), Note: Methods for solution could include substitution, linear combination, graphing focusing on pairs of linear equations in two variables. and matrices.(ND) 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 = and the circle x² + y² = 3. –3x Represent a system of linear equations as a single matrix equation in a vector Example (ND): variable. Vector Variable (+) Represent the system as a matrix equation: Solution:
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. This standard is related to HS.N-CN.7. (ND) ↑Comment: It is appropriate for all students to be able to recognize when the quadratic formula gives complex solutions. The pre-requisite for this standard is the understanding of complex numbers and their properties. (ND) Cluster: Solve systems of equations. Code Standards Annotation Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Students might “prove” by providing a formal proof, demonstrating, or justifying. See the glossary for a definition of “mathematical proof.” (ND) Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Note: Methods for solution could include substitution, linear combination, graphing and matrices.(ND) 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. (+) Represent a system of linear equations as a single matrix equation in a vector variable. Example (ND): Vector Variable Represent the system as a matrix equation: Solution: