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Quadratic Functions and Parabolas
Vertex form y=a(x−h)²+k displays the vertex (h,k) and opening direction.
How it works
Vertex form y=a(x−h)²+k displays the vertex (h,k) and opening direction. Name the quantities before calculating, keep each transformation logically equivalent, and check the result against the original conditions.
Worked example
Find the vertex of y=(x−3)²−4.
- Compare with y=a(x−h)²+k.
- Here h=3 and k=−4.
- The positive coefficient means the parabola opens upward.
The vertex is (3, −4).
Try it now
These questions come from the same validated skill generator used by the game.
Common mistakes
- Using a remembered formula without identifying what each symbol represents.
- Changing a value or condition during an intermediate step.
- Skipping the final substitution, estimate, or logical check.
Challenge
Describe how y=(x+2)²+5 is translated from y=x².
Questions learners ask
What is the key idea in quadratic functions and parabolas?
Vertex form y=a(x−h)²+k displays the vertex (h,k) and opening direction.
How should I check an answer?
Substitute it into the original conditions, check units and signs, and decide whether its size is reasonable.