#### Math - 2017-18

# AII.5 and *AII.4 - Solving Non-Linear Systems

**AII.5 ** The student will **solve
**nonlinear systems of equations, including linear-quadratic and
quadratic-quadratic, algebraically and graphically. Graphing calculators will
be used as a tool to visualize graphs and predict the number of solutions.

AII.4The student willsolvesystems of linear-quadratic and quadratic-quadratic equations, algebraically and graphically.

**Bloom's Level:** Apply

*Adopted: 2009*

### BIG IDEAS

- I can create telescope and wide-angle camera lenses, reconstruct
traffic accidents for investigation, monitor aircraft flight patterns as an air
traffic controller, analyze crimes for police officers, and work
as a seismologist or geologist.

- I will be
able to solve systems involving linear and quadratic equations, by quadratic
equations only by graphing, algebraically, and by using a calculator to
visualize the solution.

### UNDERSTANDING THE STANDARD

- Solutions of a nonlinear system of equations are
numerical values that satisfy every equation in the system.
- The coordinates of points of intersection in any
system of equations are solutions to the system.
- Real-world problems can be interpreted, represented, and solved using systems of equations.

· Quadratic equations included in this standard will only include those that can be represented as parabolas of the form where .

· Solutions of a system of equations are numerical values that satisfy every equation in the system.

· A linear-quadratic system of equations may have zero, one, or two solutions.

· A quadratic-quadratic system of equations may have zero, one, two, or an infinite number of solutions.

· The coordinates of points of intersection in any system of equations are solutions to the system.

· Practical problems can be interpreted, represented, and solved using systems of equations.### ESSENTIALS

__Systems of Linear __

All.5_{1} **Predict** the numbers of solutions to a
nonlinear system of two equations.

·
AII.4_{1} **Determine**
the number of solutions to a linear-quadratic and quadratic-quadratic system of
equations in two variables.

__Systems of Linear - Quadratic__

All.5_{2} **Solve** a linear-quadratic system of two
equations algebraically and graphically.

·
AII.4_{2} **Solve**
a linear-quadratic system of two equations in two variables algebraically and
graphically.

__Systems of Quadratic -
Quadratic__

All.5_{3} **Solve** a quadratic-quadratic system of
two equations algebraically and graphically.

·
AII.4_{3} **Solve**
a quadratic-quadratic system of two equations in two variables algebraically
and graphically.

·
AII.4_{4} **Solve**
systems of equations and **verify**
solutions of systems of equations with a graphing utility.

### KEY VOCABULARY

nonlinear,
linear, quadratic, algebraically, graphically, predict

*Updated: Oct 27, 2017*