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Algebra Difficulty 2.0 Junior Prove it Canada

The vertex of the parabola $y=(x-b)^2+b+h$ has coordinates $(2,5)$ . What is the value of $h$ ?

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.