Quadratic equation of graphs

Question

How can I express $p$ and $h$ in terms of $k$? I'm thinking of $0=-(k-p)^{2} + h$. However, there are $2$ variables in this equation, how can I get rid of one of them?

Answer 1

Write $f(x)=-(x)(x-k)=-x^2+kx$ because $0$ and $k$ are roots of $f$ and compare with $f(x)=-(x-p)^2+h=-x^2+2px-p^2+h$. That will give you

$$2p=k \Rightarrow p=k/2$$ $$-p^2+h=0 \Rightarrow h=p^2=k^2/4$$