Search the California Content Standards

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Create equations that describe numbers or relationships.

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Create equations and inequalities in one variable including ones with absolute value and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. CA *

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Create equations that describe numbers or relationships.

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Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. *

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Create equations that describe numbers or relationships.

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Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. * [Include formulas involving quadratic terms.]

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Build a function that models a relationship between two quantities. [Quadratic and exponential]

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Write a function that describes a relationship between two quantities. * Determine an explicit expression, a recursive process, or steps for calculation from a context. *

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Build a function that models a relationship between two quantities. [Quadratic and exponential]

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Write a function that describes a relationship between two quantities. * Combine standard function types using arithmetic operations. *

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Build new functions from existing functions. [Quadratic, absolute value]

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Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

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Build new functions from existing functions. [Quadratic, absolute value]

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Find inverse functions. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2x^3.

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

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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.

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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 probability to evaluate outcomes of decisions. [Introductory; apply counting rules.]

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(+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). *