Search the California Content Standards

Cluster:
Use complex numbers in polynomial identities and equations. [Quadratics with real coefficients]

Standard:
Solve quadratic equations with real coefficients that have complex solutions.

Cluster:
Use complex numbers in polynomial identities and equations. [Quadratics with real coefficients]

Standard:
(+) Extend polynomial identities to the complex numbers. For example, rewrite x^2 + 4 as (x + 2i)(x – 2i).

Cluster:
Use complex numbers in polynomial identities and equations. [Quadratics with real coefficients]

Standard:
(+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

Cluster:
Represent and solve equations and inequalities graphically. [Combine polynomial, rational, radical, absolute value, and exponential functions.]

Standard:
Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. *

Cluster:
Represent and solve equations and inequalities graphically. [Combine polynomial, rational, radical, absolute value, and exponential functions.]

Standard:
Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. *

Cluster:
Understand solving equations as a process of reasoning and explain the reasoning. [Simple radical and rational]

Standard:
Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Cluster:
Understand solving equations as a process of reasoning and explain the reasoning. [Simple radical and rational]

Standard:
Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Cluster:
Solve equations and inequalities in one variable.

Standard:
Solve one-variable equations and inequalities involving absolute value, graphing the solutions and interpreting them in context. CA

Cluster:
Build a function that models a relationship between two quantities. [Include all types of functions studied.]

Standard:
Write a function that describes a relationship between two quantities. * Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. *

Cluster:
Build a function that models a relationship between two quantities. [Include all types of functions studied.]

Standard:
Write a function that describes a relationship between two quantities. * Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. *