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Translated Parabolas
(y-k)^2=4a(x-h) has vertex (h,k); translation does not change basic shape.
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Translated Parabolas
What is it?
(y-k)^2=4a(x-h) has vertex (h,k); translation does not change basic shape.
In simple words
- (y-k)^2=4a(x-h) has vertex (h,k); translation does not change basic shape.
- Worked pattern: (y-1)^2=8(x+2) has vertex (-2,1).
- Final check: domain, sign, notation, units, and reasonableness.
Important terms
Translated parabolas: (y-k)^2=4a(x-h) has vertex (h,k); translation does not change basic shape.
What you should learn
- State the rule for translated parabolas.
- Solve a translated parabolas problem step by step.
- Check the result, restrictions, notation, and units.
Recommended for Class 12
Full school-level explanation
(y-k)^2=4a(x-h) has vertex (h,k); translation does not change basic shape.
CONCEPT AND RULE
(y-k)^2=4a(x-h) has vertex (h,k); translation does not change basic shape.
METHOD
For translated parabolas, identify the given information and required result. Select the matching definition or formula, state its conditions, substitute carefully, simplify one line at a time, and check.
WORKED EXAMPLE
(y-1)2=8(x+2) has vertex (-2,1).
COMMON MISTAKE
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
How to solve translated parabolas
How it works
- Identify the mathematical objects, givens, restrictions, and required result.
- Choose and write the relevant definition, theorem, or formula.
- Substitute with brackets and carry out one justified step per line.
- Simplify, state the final answer clearly, and verify it in the original setting.
Remember
- Translated parabolas
- rule
- worked example
- worked example
How the ideas connect
Worked example: (y-1)^2=8(x+2) has vertex (-2,1).
Deeper understanding
Go beyond memorising Translated Parabolas. Connect the definition to reasons, relationships, exceptions, and exam wording.
How the ideas connect
Worked example: (y-1)^2=8(x+2) has vertex (-2,1).
Common mistakes
Exam focus
Core Idea
Rule / Formula
Method
Worked Example
Exam focus
Quick revision
- Translated parabolas
- rule
- worked example
- Translated parabolas: (y-k)^2=4a(x-h) has vertex (h,k); translation does not change basic shape.
- CONCEPT AND RULE: (y-k)^2=4a(x-h) has vertex (h,k); translation does not change basic shape.
- METHOD: For translated parabolas, identify the given information and required result. Select the matching de
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
For long answers on Translated Parabolas: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- Translated parabolas
- rule
- worked example
- Translated parabolas: (y-k)^2=4a(x-h) has vertex (h,k); translation does not change basic shape.
Important formulas
- Translated parabolas
- rule
- worked example
Common exam traps
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
- A matching-looking formula is not valid until its conditions and domain have been checked.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
- Mistake
A matching-looking formula is not valid until its conditions and domain have been checked.
- Mistake
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
Translated parabolas
rule
worked example
Translated parabolas: (y-k)^2=4a(x-h) has vertex (h,k); translation does not change basic shape.
(y-k)^2=4a(x-h) has vertex (h,k); translation does not change basic shape.
- Definition
- (y-k)^2=4a(x-h) has vertex (h,k); translation does not change basic shape.
- Critical warning
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all d
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Exam Practice
Define
Q1. Define Translated Parabolas.
Explain
Q2. Explain: CONCEPT AND RULE.
Example
Q3. Give one clear example of Translated Parabolas and say why it fits.
Mistake
Q4. State one common mistake students make about Translated Parabolas.
Exam note
Q5. Write a short exam note on Translated Parabolas: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.