Search the California Content Standards

Cluster:
Write expressions in equivalent forms to solve problems. [Quadratic and exponential]

Standard:
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* Factor a quadratic expression to reveal the zeros of the function it defines.*

Cluster:
Write expressions in equivalent forms to solve problems. [Quadratic and exponential]

Standard:
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.*

Cluster:
Write expressions in equivalent forms to solve problems. [Quadratic and exponential]

Standard:
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15^t can be rewritten as (1.15^1/12)^12t ≈ 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.*

Cluster:
Perform arithmetic operations with complex numbers. [i^2 as highest power of i]

Standard:
Know there is a complex number i such that i^2 = −1, and every complex number has the form a + bi with a and b real.

Cluster:
Perform arithmetic operations with complex numbers. [i^2 as highest power of i]

Standard:
Use the relation i^2 = −1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

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

Standard:
Solve quadratic equations with real coefficients that have complex solutions.

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

Standard:
(+) 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]

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

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:
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. *