f(x)=-2x²+2x+4. Note the y-intercept is 4 (when x=0).
f(x)=-2(x²-x-2),
f(x)=-2(x²-x+¼-¼-2),
f(x)=-2[(x-½)²-9/4],
f(x)=9/2-2(x-½)².
From this we can see that the maximum value is 9/2 which occurs when x=½, making (½,9/2) the vertex (0.5,4.5) and x=½ or x=0.5 the axis of symmetry.
So we have a parabola shaped like an upturned U which intersects the y-axis at y=4.
To find the x intercepts, we solve f(x)=0:
f(x)=0=-2(x²-x-2)=-2(x-2)(x+1), so x=2 and x=-1 are the x-intercepts (where the parabola intersects the x-axis).
To draw the graph mark all the intercepts:
(0,4), (2,0), (-1,0) and the vertex (0.5,4.5) (the highest point). The curve must pass through all these points and must be symmetrical about the line x=0.5.