Ohio Resource Center
Content Supports - Activities and rich problems
Fireworks: The Localized Big Bang
Discipline
Mathematics
9, 10, 11, 12
Professional Commentary

Commercial fireworks must be carefully timed to ignite as intended. The process involves projectile motion that can be modeled with the quadratic function (ignoring air resistance), as found in the study of dynamics in physics: h = –16t2 + v0t + h0. We need to study the parameter-behavior connection as each parameter has real-world significance. The contextual situation will lead to the study of behaviors of the quadratic function in standard form too. This mathematically rich problem was prepared by the Ohio Resource Center to accompany the Mathematics Program Models for Ohio High Schools developed by the Ohio Department of Education. (author/sw)

Common Core State Standards for Mathematics
High School - Functions
Interpreting Functions
Analyze functions using different representations
HSF-IF.C.7
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
1. Graph linear and quadratic functions and show intercepts, maxima, and minima.
2. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
3. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
4. (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
5. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
Building Functions
Build new functions from existing functions
HSF-BF.B.3
Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
Ohio Mathematics Academic Content Standards (2001)
Patterns, Functions and Algebra Standard
Benchmarks (8–10)
C.
Translate information from one representation (words, table, graph or equation) to another representation of a relation or function.
D.
Use algebraic representations, such as tables, graphs, expressions, functions and inequalities, to model and solve problem situations.
E.
Analyze and compare functions and their graphs using attributes, such as rates of change, intercepts and zeros.