### Algebra 2 Power Standards

Power Standards- Algebra II

1. Analyze and Interpret Quadratic Equations and Functions both algebraically and graphically

For the purpose of:

• Identifying the zeros, roots, and/or factors of polynomials.

• Applying transformations of functions as related to parent functions.

• Determining relative maximum and minimum values of polynomials as coordinates and y values.

• Recognizing the different forms of quadratic functions such as vertex form y=a(x-h)^2 + k, standard form y= ax^2+bx+c, and intercept forms       y=a(x-r)(x-q)

• Using the Square root property to solve quadratic equations

• Utilizing factoring techniques when a=1 or a is not one to find zeros.

• Completing the square to solve quadratic equations when not factorable.

• Solving quadratic equations using the quadratic formula and identifying types of roots using the discriminant.

1. Identifying Imaginary numbers and Complex numbers

• Recognize the complex number i such thatand that every complex number can be written in the form a+bi.

• Perform addition, subtraction, multiplication, and division with complex numbers.

• Plot in the complex plane using x as the real axis, and y as the imaginary axis.

• Rationalize the denominator by multiplying both the numerator and denominator by a complex conjugate

3. Study polynomials and recognize the properties of graphs of different degree.

Algebra II students will be able to:

• Describe end behaviors of odd and even functions by studying the lead coefficient and degree of the polynomial. (Compare to the corresponding parent functions)

• Use the rational root theorem to find roots and zeros of polynomials.

• Utilize Descartes’ Rule of Signs to determine the number of real possible roots of a polynomial.

• Identify Zeros both algebraically and graphically.

• Factor polynomials using quadratic techniques and find roots of a polynomial.

• Apply Polynomial division (synthetic and long division, remainder theorem)

• Identify Relative/local maximum and minimum both algebraically and graphically.

• Describe Domain and Range by looking at a graph and by stating excluded values.

• Develop Composite and inverse functions given f(x) and g(x) to find f(g(x)) and g(f(x))

4.Graphing Logarithmic and Exponential Functions and understanding that

• Graph exponent and log functions
• Solve exponential equations using logarithms

• Identify and utilize properties of exponents and logarithms

• Find e and its inverse ln

• Solve problems using exponential growth and decay

5. Names of Special Functions

- Identify and graph absolute value functions

- Identify and graph piecewise-functions

- Identify and graph constant functions

- Identify and graph step functions

- Identify and graph radical functions

- Identify and graph inverse functions

6.Rational functions
• Write and solve Joint, direct, and inverse variation equations
• Perform Operations on rational functions
• Solve rational equations

• Graph rational functions