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