Between which values does the square root of 111 lie?

Step-by-step explanation:

f(x) = -16x² + 22x + 3

Factor:

f(x) = (8x + 1) (-2x + 3)

The x-intercepts are (-1/8, 0) and (3/2, 0).

The leading coefficient is negative, so the parabola points down.  Therefore, the vertex is a maximum.  The x-coordinate is halfway between the x-intercepts.

x = (-1/8 + 3/2) / 2

x = 11/16

f(11/16) = 169/16

So the vertex is at:

(11/16, 169/16)

Graph the x-intercepts and the vertex, then draw a curve through the 3 points.