Consider complex numbers, roots, and quadratic equations. Use the discriminate as a way to determine the nature of a quadratic's roots. Then discuss the similarities and differences between quadratics with two, one, or no real roots....

Your learners combine their knowledge of real and imaginary numbers and matrices in an activity containing thirty lessons, two assessments (mid-module and end module), and their corresponding rubrics. Centered on complex numbers and...

Students examine complex numbers. In this Algebra II lesson, students investigate two programs that involve complex numbers: the MANDELER Program and SYNDIV program.

Quadratic solutions come in all shapes and sizes, so help your classes find the right one! Learners use the quadratic formula to find solutions for quadratic equations. Solutions vary from one, two, and complex. 

Working with imaginary numbers — this is where it gets complex! After exploring the graph of complex numbers, learners simplify them using addition, subtraction, and multiplication. 

A solution will work one way or another: find solutions, or use solutions to find the function. Learners use polynomial identities to factor polynomials with complex solutions. They then use solutions and the Zero Product Property to...

Class members perform complex operations on a plane in the 17th segment in the 32-part series. Learners first verify that multiplication by the reciprocal does the same geometrically as it does algebraically. The class then circles back...

Students solve problems with complex numbers. In this algebra lesson, students factor complex numbers and simplify equations using DeMoivre's Theorem. They add, subtract, multiply and divide using negative roots.

Learners identify the end behavior of polynomial graphs. In this algebra lesson, students factor and solve quadratic and complex equations. They factor out negative roots and identify the real and imaginary parts of an equation.

Pupils convert quadratic functions from standard form to vertex form. In this algebra lesson, students solve polynomials using synthetic and long division. They derive and apply the remainder theorem and factor theorem.

Should matrices be allowed to commute when they are being multiplied? Learners analyze this question to determine if the commutative property applies to matrices. They connect their exploration to transformations, vectors, and complex...

The greater the degree, the more solutions to find! Individuals find the real solutions from a graph and use the Fundamental Theorem of Algebra to find the remaining factors. 

Bring some concrete reasoning to the skills of multiplying and combining terms. Using various strategies, the six activities in the module provide practice for the skills of adding, subtracting, multiplying, and diving polynomials. The...

Remember long division from fifth grade? Use the same algorithm to divide polynomials. Learners develop a strategy for dividing polynomials using what they remember from dividing whole numbers.

Students explore the concept of Mandelbrot sets and Julia sets. For this Mandelbrot and Julia set lesson, students use a function integrator applet to investigate two-variable function iterations. Students use Julia set and Mandelbrot...

These four problems will guide your class through the idea behind the Fundamental Theorem of Algebra, which states that a polynomial of degree n has exactly n roots. Use the division algorithm and the definition of a zero/root of a...

In this real-world example, algebra learners start to get a sense of how to represent the relationship between two variables in different ways. They start by looking at a partial table of values that define a linear relationship. They...

Students solve and graph quadratic equations. In this algebra lesson, students perform basic operation using addition, subtraction, multiplication and division. They compute the quadratic formula.

Show your class how people calculated complex math problems in the old days. Scholars take a trip back to the days without calculators in the 15th installment of a 35-part module. They use logarithms to determine products of numbers and...

Students factor polynomials and use long division t solve problems. In this algebra lesson, students find the zeros of polynomials by synthetic and long division. They perform operation using complex numbers.

Many learners find completing the square the preferred approach to solving quadratic equations. Class members combine their skills of using square roots to solve quadratics and completing the square. The resource incorporates a...

Patterns in polygons lead to patterns in polynomials. Presented with a series of polygons, individuals create polynomial expressions to represent their patterns. The algebra project consists of nine problems that incorporate polynomial...

Young mathematicians explore the maximun area for patio with the added complexity of finding the mimimum cost for construction. First, they maximize the area of a yard given a limited amount of fence and  plot width v. area on a...

Students investigate the properties behind the quadratic equation. In this algebra lesson, students identify quadratic equation in the real world. They graph the parabola and identify the vertex and intercepts.