Question

Find the vertex of the parabola whose equation is y = -2x2 + 8x - 5.



(2, 3)

(2, 19)

(2, 27)

Answer 1

vertex formula: \(\Large \color{blue}{y=a(x-h)^2+k}\) with \(\Large (h,k)\) is vertex

\(\Large y=a(x-h)^2+k=a(x^2-2xh+h^2)+k\\\Large =(a)x^2+(-2ah)x+(ah^2+k)\)

Here equation is \(\Large y = -2x^2 + 8x - 5\).Thus:
\(\Large a=-2\\\Large -2ah=8\\\Large ah^2+k=-5\)

Therefore: \(\Large h=2\ and\ k=3\)
So the vertex \(\Large (h,k)=(2,3)\)