Find the relative maxima and minima of y by the second-derivative test

Question

Find the relative maxima and minima of y by the second-derivative test $$y=−2x^2+8x+25$$

So far I've done: $$ \begin{align} f'(x)&=-4x+8 \\ f''(x)&=-4 \end {align} $$

Then $$ \begin{align} f'(x)&=0 \\ -4x+8&=0 \\ x&=2 \end{align} $$

Not sure what to do from here...

Answer 1

At $x=2$, $f''(x)=-4$, which is negative, so $x=2$ is a maximum point