This problem is sure to get your young mathematicians thinking. The idea sounds simple: one equation, solve it as many ways as you can. This is meant to get at a deeper understanding of solving quadratic equations, including some more...

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....

Explore nonlinear systems through graphs and algebra. High schoolers begin by examining the different types of quadratic functions and their possible intersections. They then use algebraic methods to solve systems containing various...

The equations look different, but their graphs are the same. How can that be? This activity leads your mathematicians in an exploration of three different forms of the same quadratic function. After comparing the equations, their graphs,...

What does completing the square have to do with circles? Math pupils use completing the square and other algebraic techniques to rewrite equations of circles in center-radius form. They then analyze equations of the form x^2 + y^2 + Ax +...

When is finding the discriminant enough? Using the quadratic formula helps find solutions to quadratic equations, but there are times when just using the discriminant is appropriate. Use this algebra II lesson to help classes see...

Tackle a common misconception using a performance task. Dividing by a variable to eliminate a variable may seem like a good idea, but simplifying the variable eliminates solutions as well. Learners develop algebraic and graphical support...

Challenge algebra learners to use the difference of cubes to solve this problem. Once your charges have taken out the factor (a - b), combined the like terms and set them equal to zero, the problem becomes a factorable quadratic...

Investigate the Fundamental Theorem of Algebra and explore polynomial equations to determine the number of factors, the number of roots, and investigate multiplicity of roots.

Use a one-stop resource for everything you'd possibly want to teach about quadratic functions and models. Scholars analyze key features of quadratic functions as well as transformations of functions through seven activities....

How can baseball and skeet-shooting be modeled mathematically? Sports lovers and young mathematicians learn how to use quadratic equations and systems of equations to model the flight paths of various objects.

Use an activity to illustrate the different forms of a quadratic function. Here, the task asks learners to use composition of given functions to build an explicit function. The process emphasizes the impact of the order of...

Read between the curves ... quadratic curves! Young scholars analyze the graphs of two quadratic functions by writing their own function whose outputs are between the two given. They then consider intersecting quadratic functions and...

Relate factors to zeros and x-intercepts. Scholars first graph quadratics in both standard and factored forms to see that they are the same. They go on to use the graphs to see the relationship between factors and x-intercepts.

This activity uses the division algorithm and the definition of a zero/root of a function to guide your class to see the relationship between zeros and factors of a general quadratic, which can later be generalized to the Remainder...

This is a wonderful exercise for learners to apply their critical thinking skills along with their knowledge of quadratic functions and parabolas. Young mathematicians investigate a real-world scenario about the height a baseball reaches...

Linear, quadratic, and exponential functions are represented only by their table of values in this simple, well-written activity. Learners decide the type of graph represented based on the differences in the function values....

It's all in the numbers! Create a mathematical model to analyze a number game and develop a winning strategy. Using a given numerical pattern, scholars write an expression to model the scenario. They then interpret the pattern of the...

This fun activity guides learners through an exploration of the effects of replacing f(x) with -f(x), f(x) + c, k f(x), and f(x + c). Using graphing calculators, students experiment with variations of the graph of y = x^2 to design a...

Weight is a function of the distance from sea level. Learners explore the many implications of this fact in an inquiry-based task. Given the function, pupils answer questions before manipulating the function to rewrite the distance...

Don't let a little challenge get between your pupils and their learning! Scholars compare two absolute value functions to recognize patterns and use them to build their own functions with outputs that are between the given. They then...

Adjust this instructional activity to fit either beginning or more advanced learners. Build a scatter plot, determine appropriate model (linear, quadratic, exponential), and then extend to evaluate the model with residuals. This problem...

Using their Ti-Nspire to determine the solutions of parabolas, students explore the concept of complex roots.  Students determine if parabolas have real or complex roots.  Students determine the the axis of symmetry and the...

Paper folding, flu spreading in a school, bacteria growth, and continuously compounded interest all provide excellent models to study exponential functions. This is a comprehensive resource that looks at many different aspects of...