EDUCATION DECISION WORKBENCH
Explore quadratic, absolute-value, and exponential transformations with equations, landmarks, domain, range, and generated values.
Review output
Load the worked example to inspect realistic inputs, or enter anonymous, policy-approved information. Results remain in this browser tab until you copy or download them.
Transparent method
The model is y = a f(x − h) + k. Quadratic uses f(u)=u², absolute value uses f(u)=|u|, and exponential uses f(u)=2ᵘ. Multiplying by a scales all parent outputs vertically and reflects them when a is negative. Replacing x by x − h shifts the graph h units horizontally, and adding k shifts every output vertically. For quadratic and absolute value, (h, k) is the vertex or turning point and the sign of a determines whether values extend upward or downward. For a base-two exponential, y = k is the horizontal asymptote and the sign of a determines which side contains the range. All three implemented parent functions have all real x in their mathematical domain.
Confirm the question, variables, units, source data, measurement precision, and the model expected by the current course or laboratory. Keep an untouched copy of observations before excluding or transforming any value.
Run the worked example first, inspect every intermediate row, compare units and signs, and look for a result that conflicts with the graph, physical system, chemical equation, or learning objective.
Record the method, assumptions, units, rounding, data limitations, and any excluded observations. Compare the exported report with an independent calculation or approved reference before assessment or laboratory use.
How to interpret the result
Use this explorer when learning how parameters change a familiar parent graph or when checking a hand-built table before plotting. It connects symbolic form with vertex, turning point, asymptote, reflection, vertical scale, domain, and range. It does not replace solving a contextual problem, choosing an appropriate function family, or checking restrictions from the original situation.
The worked quadratic uses a = −2, h = 3, and k = 5. The report writes y = −2(x − 3)² + 5, identifies vertex (3, 5), states that the graph opens downward and has range y ≤ 5, then evaluates symmetric x values around 3 so the learner can see equal outputs at equal horizontal distances.
The model is y = a f(x − h) + k. Quadratic uses f(u)=u², absolute value uses f(u)=|u|, and exponential uses f(u)=2ᵘ. Multiplying by a scales all parent outputs vertically and reflects them when a is negative. Replacing x by x − h shifts the graph h units horizontally, and adding k shifts every output vertically.
For quadratic and absolute value, (h, k) is the vertex or turning point and the sign of a determines whether values extend upward or downward. For a base-two exponential, y = k is the horizontal asymptote and the sign of a determines which side contains the range. All three implemented parent functions have all real x in their mathematical domain.
Do not reverse the horizontal shift, treat a as a horizontal scale, claim an exponential graph reaches its asymptote, omit parentheses around x − h, or use a = 0 when discussing a transformed parent family. Check intercepts, symmetry, end behavior, domain restrictions from context, axis scale, and whether the chosen function type fits the supplied relationship.
Learning boundary
This browser-local workbench calculates only from the entered model and observations. It cannot validate an experiment, balance an equation, establish causation, certify laboratory safety, diagnose learning, or replace the method required by a teacher, curriculum, laboratory, or institution.
Review checklist
Practical questions
No. The calculation runs in the current browser tab. Avoid personal information and retain laboratory data in the system authorized by the school.
Treat it as an editable analysis aid. Show your own reasoning, cite the required sources, follow academic-integrity rules, and use the method requested by your course.
No. Check dimensions, graph shape, assumptions, measurement uncertainty, significant figures, and whether another model explains the observations better.
YOUR NIRMION
