This task has students explore the relationship between the three parameters a, b, and c in the equation f(x)=ax2+bx+c and the resulting graph. There are many possible approaches to solving each part of this problem, especially the first part.

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

This task requires students to determine whether a number is rational or irrational. The task assumes that students are able to express a given repeating decimal as a fraction.

The purpose of this task is to use the definition of rotations in order to find the center and angle of rotation given a triangle and its image under a rotation.

The purpose of this task is to study the impact of translations on triangles.

The goal of this task is to get students to focus on the shape of the graph of an equation and how this changes depending on the sign of the exponent and on whether the exponential is in the numerator or denominator.

In this task, students use trigonometric functions to model the movement of a point around a wheel and, in the case of part (c), through space (F-TF.5). Students also interpret features of graphs in terms of the given real-world context (F-IF.4).

This task asks students to interpret the relevant parameters in terms of the real-world context and describe exponential growth.

This is a direct task suitable for the early stages of learning about exponential functions. Students interpret the relevant parameters in terms of the real-world context and describe exponential growth.

This problem assumes students have completed several preliminary tasks about the fact that linear functions change by equal differences over equal intervals.

Students are asked to consider the expression that arises in physics as the combined resistance of two resistors in parallel. However, the context is not explicitly considered here. The task is good general preparation for problems more specifically aligned to either A-SSE.1 or A-SSE.2.

This Illustrative Mathematics task encourages students to reason quantitatively about the structure of the expression.

The purpose of this task is to help students see manipulation of expressions as an activity undertaken for a purpose. The expression arises in physics as the reciprocal of the combined resistance of two resistors in parallel. However, the context is not explicitly considered here.
Variation 1 of this task presents a related more complex expression already in the correct form to answer the question.

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

The goal of this task is to provide a introduction to the sometimes subtle use of density and units related to density, in a simple and fun context with minimal geometric complexity.

The purpose of this task is to probe students' ability to correlate symbolic statements about a function using function notation with a graph of the function, and to interpret their answers in terms of the quantities between which the function describes a relationship

The principal purpose of this task is to probe students' ability to correlate symbolic statements about a function using function notation with a graph of the function, and to interpret their answers in terms of the quantities between which the function describes a relationship.

This task shows how to inscribe a circle in a triangle using angle bisectors. A companion task, ``Inscribing a circle in a triangle II'' stresses the auxiliary remarkable fact that comes out of this task, namely that the three angle bisectors of triangle ABC all meet in the point O.

This task is primarily for instructive purposes but can be used for assessment as well. Parts (a) and (b) are good applications of geometric constructions using a compass and could be used for assessment purposes but the process is a bit long since there are six triangles which need to be constructed.

This task provides an opportunity for students to apply triangle congruence theorems in an explicit, interesting context.