Search the California Content Standards

Cluster:
Perform arithmetic operations on polynomials. [Polynomials that simplify to quadratics]

Standard:
Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Cluster:
Create equations that describe numbers or relationships.

Standard:
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 *

Cluster:
Create equations that describe numbers or relationships.

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

Cluster:
Create equations that describe numbers or relationships.

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

Cluster:
Solve equations and inequalities in one variable. [Quadratics with real coefficients]

Standard:
Solve quadratic equations in one variable. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)^2 = q that has the same solutions. Derive the quadratic formula from this form.

Cluster:
Solve equations and inequalities in one variable. [Quadratics with real coefficients]

Standard:
Solve quadratic equations in one variable. Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

Cluster:
Solve systems of equations. [Linear-quadratic systems]

Standard:
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x^2 + y^2 = 3.

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

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

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

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

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

Standard:
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.