MA.912.AR.3.8

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Solve and graph mathematical and real-world problems that are modeled with quadratic functions. Interpret key features and determine constraints in terms of the context.

Examples

Algebra 1 Example: The value of a classic car produced in 1972 can be modeled by the function begin mathsize 12px style V open parentheses t close parentheses equals 19.25 t squared minus 440 t plus 3500 end style, where t is the number of years since 1972. In what year does the car’s value start to increase?

Clarifications

Clarification 1: Key features are limited to domain; range; intercepts; intervals where the function is increasing, decreasing, positive or negative; end behavior; vertex; and symmetry.

Clarification 2: Instruction includes the use of standard form, factored form and vertex form.

Clarification 3: Instruction includes representing the domain, range and constraints with inequality notation, interval notation or set-builder notation.

Clarification 4: Within the Algebra 1 course, notations for domain, range and constraints are limited to inequality and set-builder.

General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 912
Strand: Algebraic Reasoning
Standard: Write, solve and graph quadratic equations, functions and inequalities in one and two variables.
Date Adopted or Revised: 08/20
Status: State Board Approved

Related Courses

This benchmark is part of these courses.
1200310: Algebra 1 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1200320: Algebra 1 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1200330: Algebra 2 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1200340: Algebra 2 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1200380: Algebra 1-B (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7912090: Access Algebra 1B (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))
1200315: Algebra 1 for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1200385: Algebra 1-B for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7912075: Access Algebra 1 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))
7912095: Access Algebra 2 (Specifically in versions: 2016 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))
1200388: Mathematics for Data and Financial Literacy Honors (Specifically in versions: 2022 and beyond (current))
1200710: Mathematics for College Algebra (Specifically in versions: 2022 and beyond (current))
1209315: Mathematics for ACT and SAT (Specifically in versions: 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.912.AR.3.AP.8: Given a mathematical and/or real-world problem that is modeled with quadratic functions, solve the mathematical problem, or select the graph using key features (in terms of context) that represents this model.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Formative Assessments

Model Rocket:

Students are asked to graph a function in two variables given in context.

Type: Formative Assessment

Rocket Town:

Students are asked to rewrite a quadratic expression in vertex form to find maximum and minimum values.

Type: Formative Assessment

Jumping Dolphin:

Students are asked to find the zeros of a quadratic function in the context of a modeling problem.

Type: Formative Assessment

Lesson Plan

Parts and more Parts-- Parabola Fun:

This is an entry lesson into quadratic functions and their shapes. Students see some real-life representations of parabolas. This lesson provides important vocabulary associated with quadratic functions and their graphs in an interactive manner. Students create a foldable and complete a worksheet using their foldable notes.

Type: Lesson Plan

Perspectives Video: Experts

Jumping Robots and Quadratics:

Jump to it and learn more about how quadratic equations are used in robot navigation problem solving!

Type: Perspectives Video: Expert

Using Mathematics to Optimize Wing Design:

Nick Moore discusses his research behind optimizing wing design using inspiration from animals and how they swim and fly.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Problem Solving with Project Constraints:

It's important to stay inside the lines of your project constraints to finish in time and under budget. This NASA systems engineer explains how constraints can actually promote creativity and help him solve problems!

Type: Perspectives Video: Expert

Perspectives Video: Professional/Enthusiast

Quadratic Equations and Robots:

Get in gear with robotics as this engineer explains how quadratic equations are used in programming robotic navigation.

Type: Perspectives Video: Professional/Enthusiast

Tutorial

Graphing Quadratic Equations:

This tutorial helps the learners to graph the equation of a quadratic function using the coordinates of the vertex of a parabola and its x- intercepts.

Type: Tutorial

MFAS Formative Assessments

Jumping Dolphin:

Students are asked to find the zeros of a quadratic function in the context of a modeling problem.

Model Rocket:

Students are asked to graph a function in two variables given in context.

Rocket Town:

Students are asked to rewrite a quadratic expression in vertex form to find maximum and minimum values.

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Perspectives Video: Experts

Jumping Robots and Quadratics:

Jump to it and learn more about how quadratic equations are used in robot navigation problem solving!

Type: Perspectives Video: Expert

Problem Solving with Project Constraints:

It's important to stay inside the lines of your project constraints to finish in time and under budget. This NASA systems engineer explains how constraints can actually promote creativity and help him solve problems!

Type: Perspectives Video: Expert

Perspectives Video: Professional/Enthusiast

Quadratic Equations and Robots:

Get in gear with robotics as this engineer explains how quadratic equations are used in programming robotic navigation.

Type: Perspectives Video: Professional/Enthusiast

Tutorial

Graphing Quadratic Equations:

This tutorial helps the learners to graph the equation of a quadratic function using the coordinates of the vertex of a parabola and its x- intercepts.

Type: Tutorial

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

Perspectives Video: Expert

Problem Solving with Project Constraints:

It's important to stay inside the lines of your project constraints to finish in time and under budget. This NASA systems engineer explains how constraints can actually promote creativity and help him solve problems!

Type: Perspectives Video: Expert

Perspectives Video: Professional/Enthusiast

Quadratic Equations and Robots:

Get in gear with robotics as this engineer explains how quadratic equations are used in programming robotic navigation.

Type: Perspectives Video: Professional/Enthusiast