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.

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

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

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

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

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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]

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

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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.

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Solve equations and inequalities in one variable.

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

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Apply geometric concepts in modeling situations.

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Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). *

Cluster:
Apply geometric concepts in modeling situations.

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Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). *