**Critical Point Method**
**Step 3:** Find the functions zeros by solving f(x) = 0.

f(x) = -x^{2} + 2x + 3

(-x + 3)(x+1) = 0

x = 3, -1.

**Step 4:** Find the critical points of the function by solving f'(x) = 0. Determine over which intervals the function is increasing or decreasing.

f'(x) = -2x +2 = 0

x = 1

f(x) is increasing over x = -infinity to 1 since f'(x) is positive there, and is decreasing over x = 1 to infinity since f'(x) is negative there.

**Step 5:** Find the inflection points of the function by solving f''(x) = 0. Determine over which intervals the function is concave up or down.

f''(x) = -2 so there are no inflection points.

**Step 6:** Calculate some y values of the function at one or two convenient x values. Proceed to draw the graph using information you have gathered.