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BetterGrades Algebra · Unit A9 · Unit Hub

Unit A9: Quadratic Functions and Models

Connect quadratic equations to parabola geometry, modeling, and optimization. What does each algebraic form reveal about a parabola?

Act IX - One nonlinear object, several useful forms

The 8-lesson path

The same quadratic appears in standard, factored, and vertex forms. Students learn to choose a form based on the information needed, then use parabolas for modeling, inequalities, and regression.

Governing question

What does each algebraic form reveal about a parabola?

Connect quadratic equations to parabola geometry, modeling, and optimization.

Mastery design

Know when to continue

Students select and convert forms, graph from structure, solve inequalities, and interpret an optimum with units.

Unit outcomes
  1. Identify vertex, axis, intercepts, opening, and extremum.
  2. Interpret standard, factored, and vertex forms.
  3. Convert among forms strategically.
  4. Build and interpret quadratic models.
  5. Solve quadratic inequalities and critique quadratic fits.
Core sequence

Lessons

Move in order when this material is new; use prerequisites and repair links when entering mid-unit.

  1. 01Quadratic relations and three useful formsUnderstand that standard, factored, and vertex forms expose different features of one function.
  2. 02Graphing parabolasUse opening, scale, symmetry, vertex, and intercepts to construct a graph.
  3. 03Factored form and zerosConnect factors, roots, sign changes, and horizontal intercepts.
  4. 04Vertex form and transformationsRead shifts, scale, and extrema from a(x−h)2+ka(x-h)^2+k.
  5. 05Moving among formsFactor, expand, or complete the square according to the question being asked.
  6. 06Quadratic models and extremaInterpret the vertex as a maximum or minimum in context.
  7. 07Quadratic inequalitiesCombine zeros, sign intervals, and graph position to find solution regions.
  8. 08Quadratic regression and model limitationsFit curved data and compare model quality without mistaking fit for causation.

Practice around the path

Review, mixed practice, mastery, and investigation

Every route contains a fixed set of concrete questions, with detailed solutions available after an attempt.

ReviewCumulative reviewRevisit this unit with prior-unit retrieval.PracticeMixed practiceClassify the structure before choosing a method.MasteryMastery checkUse the supplied grading and cumulative-share contract.InvestigationPerformance taskBuild and optimize an area, revenue, or projectile model and interpret all mathematically valid roots.Response guideMastery response guideAttempt-gated rubric support; no invented canonical answers.

Source & rights

Original storyboard, rights-separated references.

Public page content comes from the BetterGrades Algebra editorial storyboard supplied by the owner. Reference books named in provenance remain separate and are not copied into the application.