Search the California Content Standards

Cluster:
Construct and compare linear, quadratic, and exponential models and solve problems.

Standard:
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). *

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Construct and compare linear, quadratic, and exponential models and solve problems.

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Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. *

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Construct and compare linear, quadratic, and exponential models and solve problems. [Linear and exponential]

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Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. *

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Interpret expressions for functions in terms of the situation they model. [Linear and exponential of form f(x) = b^x + k]

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Interpret the parameters in a linear or exponential function in terms of a context. *

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Interpret expressions for functions in terms of the situation they model.

Standard:
Interpret the parameters in a linear or exponential function in terms of a context. * [Linear and exponential of form f(x) = b^x + k]

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Interpret expressions for functions in terms of the situation they model.

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Apply quadratic functions to physical problems, such as the motion of an object under the force of gravity. CA *

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Use coordinates to prove simple geometric theorems algebraically. [Include distance formula; relate to Pythagorean Theorem.]

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Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).

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Use coordinates to prove simple geometric theorems algebraically. [Include distance formula; relate to Pythagorean Theorem.]

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Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

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Use coordinates to prove simple geometric theorems algebraically. [Include distance formula; relate to Pythagorean Theorem.]

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Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. *

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Know that there are numbers that are not rational, and approximate them by rational numbers.

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Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.