Search the California Content Standards

Cluster:
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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Translate between the geometric description and the equation for a conic section.

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Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

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Translate between the geometric description and the equation for a conic section.

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Derive the equation of a parabola given a focus and directrix.

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Use coordinates to prove simple geometric theorems algebraically.

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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). [Include simple circle theorems.]