Solution assignment 08 Quadratic functions and graphs

For which value of $p$ does the top of the parabola:

$y=x^2+2x-p$

lie on the line:

$y=3x$

The top of the parabola lies on the symmetry axis and thus for the $x$ -coordinate we have:

$x_{top}=-\displaystyle\frac{2}{2}=-1$

and thus:

$(x_{top},y_{top})=(-1,-1-p)$

This point must lie on the line:

$y=3x$

and thus:

$-1-p=-3$

$p=2$