• This course addresses content from the Minnesota State Math Standards and Benchmarks for the high school algebra strand.  Each standard or benchmark is identified by a set of numbers, as shown below.  Some benchmarks may be addressed in more than one unit, so the benchmark number will appear more than once.  Support resources for each standard or benchmark can be found by clicking on the benchmark number to navigate to that respective page.

### Intermediate Algebra - Trimester B Content

Unit 4 - Situations that can be modeled with quadratic functions

• 9.2.1.3  Find the domain of a function defined symbolically, graphically or in a real-world context.
• 9.2.1.4  Obtain information and draw conclusions from graphs of functions and other relations.
• 9.2.1.5  Identify the vertex, line of symmetry and intercepts of the parabola corresponding to a quadratic function, using symbolic and graphical methods when the function is expressed in the form:
f(x)=ax²+bx+c, in the form f(x)=a(x-h)²+k, or in factored form.
• 9.2.2.3  Sketch graphs of linear, quadratic and exponential functions, and translate between graphs, tables, and symbolic representations. Know how to use graphing technology to graph these functions.
• 9.2.3.2  Add, subtract and multiply polynomials; divide a polynomial by a polynomial of equal or lower degree.
• 9.2.3.3  Factor common monomial factors from polynomials, factor quadratic polynomials, and factor the difference of two squares.
• 9.2.4.1  Represent relationships in various contexts using quadratic equations and inequalities. Solve quadratic equations and inequalities by appropriate methods including factoring, completing the square, graphing and the quadratic formula. Find non-real complex roots when they exist. Recognize that a particular solution may not be applicable in the original context. Know how to use calculators, graphing utilities or other technology to solve quadratic equations and inequalities.

Unit 5 -  Solving quadratic equations (with real and imaginary solutions)

• 9.2.3.3  Factor common monomial factors from polynomials, factor quadratic polynomials, and factor the difference of two squares.
• 9.2.3.5  Check whether a given complex number is a solution of a quadratic equation by substituting it for the variable and evaluating the expression, using arithmetic with complex numbers.
• 9.2.4.1  Represent relationships in various contexts using quadratic equations and inequalities. Solve quadratic equations and inequalities by appropriate methods including factoring, completing the square, graphing and the quadratic formula. Find non-real complex roots when they exist. Recognize that a particular solution may not be applicable in the original context. Know how to use calculators, graphing utilities or other technology to solve quadratic equations and inequalities.
• 9.2.4.3  Recognize that to solve certain equations, number systems need to be extended from whole numbers to integers, from integers to rational numbers, from rational numbers to real numbers, and from real numbers to complex numbers. In particular, non-real complex numbers are needed to solve some quadratic equations with real coefficients.