The highlighted evidence outcomes are the priority for all students, serving as the essential concepts and skills. It is recommended that the remaining evidence outcomes listed be addressed as time allows, representing the full breadth of the curriculum.

Students Can (Evidence Outcomes):

Big Ideas Algebra 1 Chapters 8-9 focus on the family of quadratic functions. Consult Algebra 1 Families of Functions for additional evidence outcomes that apply to quadratic functions.

HS.A-SSE.B. Seeing Structure in Expressions: Write expressions in equivalent forms to solve problems. 

• Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.⭑ (CCSS: HS.A-SSE.B.3)

  • Factor a quadratic expression to reveal the zeros of the function it defines. (CCSS: HS.A-SSE.B.3.a)

  • Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. (CCSS: HS.A-SSE.B.3.b) 

HS.A-APR.A. Arithmetic with Polynomials & Rational Expressions: Perform arithmetic operations on polynomials. 

• Explain that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. (CCSS: HS.A-APR.A.1)

HS.A-REI.B. Reasoning with Equations & Inequalities: Solve equations and inequalities in one variable. 

• Solve quadratic equations in one variable. (CCSS:HS.A-REI.B.4)

  • Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x − p)2 = q that has the same solutions. Derive the quadratic formula from this form. (CCSS: HS.A-REI.B.4.a) 

  • Solve quadratic equations (e.g., for x2 = 49) by inspection, taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. (CCSS: HS.A-REI.B.4.b) 

HS.F-IF.C. Interpreting Functions: Analyze functions using different representations.

• Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.⭑ (CCSS: HS.F-IF.C.7)

  • Graph quadratic functions and show intercepts, maxima, and minima. (CCSS: HS.F-IF.C.7.a)

• Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. (CCSS: HS.F-IF.C.8)

  • Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. (CCSS: HS.F-IF.C.8.a)

HS.F-LE.A. Linear, Quadratic & Exponential Models: Construct and compare linear, quadratic, and exponential models and solve problems.⭑ 

• Use graphs and tables to describe that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. (CCSS: HS.F-LE.A.3)

A star symbol (⭑) represents grade level expectations and evidence outcomes that make up a mathematical modeling standards category.

Assessments:

• Chapter 7 Assessment (PDF), Chapter 8 Assessment (PDF), Chapter 9 Assessment (PDF)

• Quadratic Functions Benchmark Assessment (PDF)

• SAT Suite Educator Question Bank (Content Domain: Advanced Math)

• Additional Assessment Tasks

Instructional Resources & Notes:

• Big Ideas Algebra 1 Chapters 7-9 (skip Lessons 9.1, 9.6)

• Supplemental Lesson Resources: Chapter 7, Chapter 8, Chapter 9

• Additional Modeling Tasks

  • Get Your Hamburgers Here!, Skeleton Tower, Table Tiling, Sidewalk Stones, Patchwork, Pen the Pups!, Population Predictions, Designing a Fountain (References: Completing the Modeling Cycle, Advice on Modeling)

• Notes: 

  • Students are not expected to simplify radicals in Algebra 1, yet some of the exercises in Chapter 9 will show answers expressed as simplified square roots in the Teaching Edition and Worked-Out Solutions Key. If time allows, teachers may include the Product Property of Square Roots and the Quotient Property of Square Roots from Lesson 9.1 (Properties of Radicals); otherwise, unsimplified square roots or decimal approximations are acceptable.

  • Chapter 10 (Radical Functions and Equations) addresses evidence outcomes in Algebra 2. Chapter 10 should be skipped.