This task has students explore the relationship between the three parameters a, h, and k in the equation f(x)=a(x−h)^2+k and the resulting graph.

Article explains how trig functions are found in relation to the triangles angle measures.

Students will calculate the experimental probability of winning a basketball game by shooting two free-throws using a random integer simulation.

This video shows how to construct the incenter and incircle of a triangle.

Students might infer the answer from numerical trials like this, and such trials could help students think about the structure of the expression. To truly engage with the task, students should reason quantitatively about the structure of the expression, as in the solution.

The purpose of this task is to help students see manipulation of expressions as an activity undertaken for a purpose.

In this Khan Academy activity, students will find the measure of an angle in a circle given an inscribed angle.

In this Khan Academy activity, students are given an inscribed shape in a circle and find the length of a line segment, measure of an arc, or the measure of an angle.

This problem introduces the circumcenter of a triangle and shows how it can be used to inscribe the triangle in a circle. It also shows that there cannot be more than one circumcenter.

In this Khan Academy activity, students will interpret the change in exponential models.

In this Khan Academy activity, students will interpret the change in exponential models evaluating the function at a certain point.

In this Khan Academy activity, students will interpret the change in exponential models by finding what input value provides the result.

In this Khan Academy activity, students will interpret time in exponential models by finding what input value provides the result.

This video interprets the intersection point of the graphs of functions f and g as the solution of the equation f(x)=g(x).

This video finds the coordinates of points on a graph that are solutions to a given equation.

This task could serve as an introduction to polynomials or as an application after students are familiar with this type of function. As an introduction to polynomials the first part of the task could be done as a classroom discussion. If students are already familiar with exponential functions, the set up of the task, i.e. the balance in a bank account, might seem familiar. This task illustrates that if we vary the interest rate rather than the time we get a different type of function to model the balance in a bank account.

In this article, students become familiar with the idea that they can add, subtract, multiply, or divide two functions together to make a new function.

In this webpage, students learn what the inverse of a function is, and how to evaluate inverses of functions that are given in tables or graphs.