Find the directrix of the parabola with equation $y=-0.5x^2+2x+2$

Question

Find the directrix of the parabola with equation $$y=-0.5x^2+2x+2$$

I did this:

$$a=-0.5, b = 2, c = 2$$

Formula for the directrix is:

$$y=-1/(4a)$$

$$y=-1/(4\cdot(-0.5))=3.5$$

This is not right:

What went wrong? What is the proper way to do it?

Answer 1

Complete the square $$\begin{aligned} y&=-0.5x^2+2x+2\\ &=-0.5(x^2-4x)+2\\ &=-0.5(x^2-4x+4-4)+2\\ &=-0.5[(x-2)^2-4]+2\\&=-0.5(x-2)^2+4\end{aligned}$$ or equivalently $$y-4=-0.5(x-2)^2.$$ The directrix is given by $$y-4=-\frac{1}{4a}\quad \text{with}\; a=-0.5$$ or $$y=4+\frac{1}{2}$$