Question 824957
<pre>
Get the intercepts:

g(x) = -x²+x+6
g(0) = -0²+0+6
g(0) = 6

So the y-intercept is (0,6)

      g(x) = -x²+x+6
         0 = -x²+x+6
    x²-x-6 = 0
(x-3)(x+2) = 0
  x-3=0; x+2=0
    x=3;   x=-2

So the x intercepts are (3,0) and (-2,0)

Plot those points:

{{{drawing(1800/7,400,-4,5,-7,7,graph(1800/7,400,-4,5,-7,7),
circle(-2,0,0.15),circle(-2,0,0.13),circle(-2,0,0.11),circle(-2,0,0.09),circle(-2,0,0.07),circle(-2,0,0.05),circle(-2,0,0.03),circle(-2,0,0.01),

circle(0,6,0.15),circle(0,6,0.13),circle(0,6,0.11),circle(0,6,0.09),circle(0,6,0.07),circle(0,6,0.05),circle(0,6,0.03),circle(0,6,0.01),

circle(3,0,0.15),circle(3,0,0.13),circle(3,0,0.11),circle(3,0,0.09),circle(3,0,0.07),circle(3,0,0.05),circle(3,0,0.03),circle(3,0,0.01) )}}}


Get some more points:

 x| y
-3|-6
-1| 4
 1| 6
 2| 4
 4|-6

{{{drawing(1800/7,400,-4,5,-7,7, graph(1800/7,400,-4,5,-7,7),
circle(-2,0,0.15),circle(-2,0,0.13),circle(-2,0,0.11),circle(-2,0,0.09),
circle(-2,0,0.07),circle(-2,0,0.05),circle(-2,0,0.03),circle(-2,0,0.01),

circle(0,6,0.15),circle(0,6,0.13),circle(0,6,0.11),circle(0,6,0.09),
circle(0,6,0.07),circle(0,6,0.05),circle(0,6,0.03),circle(0,6,0.01),

circle(3,0,0.15),circle(3,0,0.13),circle(3,0,0.11),circle(3,0,0.09),
circle(3,0,0.07),circle(3,0,0.05),circle(3,0,0.03),circle(3,0,0.01),

circle(4,-6,0.15),circle(4,-6,0.13),circle(4,-6,0.11),circle(4,-6,0.09),
circle(4,-6,0.07),circle(4,-6,0.05),circle(4,-6,0.03),circle(4,-6,0.01),


circle(-3,-6,0.15),circle(-3,-6,0.13),circle(-3,-6,0.11),
circle(-3,-6,0.09),circle(-3,-6,0.07),circle(-3,-6,0.05),
circle(-3,-6,0.03),circle(-3,-6,0.01),

circle(-1,4,0.15),circle(-1,4,0.13),circle(-1,4,0.11),circle(-1,4,0.09),
circle(-1,4,0.07),circle(-1,4,0.05),circle(-1,4,0.03),circle(-1,4,0.01),

circle(1,6,0.15),circle(1,6,0.13),circle(1,6,0.11),circle(1,6,0.09),
circle(1,6,0.07),circle(1,6,0.05),circle(1,6,0.03),circle(1,6,0.01),

circle(2,4,0.15),circle(2,4,0.13),circle(2,4,0.11),circle(2,4,0.09),
circle(2,4,0.07),circle(2,4,0.05),circle(2,4,0.03),circle(2,4,0.01) )}}}{{{matrix(5,1,Then,sketch,in,the,curve)}}}{{{drawing(1800/7,400,-4,5,-7,7, graph(1800/7,400,-4,5,-7,7,-x^2+x+6),
circle(-2,0,0.15),circle(-2,0,0.13),circle(-2,0,0.11),circle(-2,0,0.09),
circle(-2,0,0.07),circle(-2,0,0.05),circle(-2,0,0.03),circle(-2,0,0.01),

circle(0,6,0.15),circle(0,6,0.13),circle(0,6,0.11),circle(0,6,0.09),
circle(0,6,0.07),circle(0,6,0.05),circle(0,6,0.03),circle(0,6,0.01),

circle(3,0,0.15),circle(3,0,0.13),circle(3,0,0.11),circle(3,0,0.09),
circle(3,0,0.07),circle(3,0,0.05),circle(3,0,0.03),circle(3,0,0.01),

circle(4,-6,0.15),circle(4,-6,0.13),circle(4,-6,0.11),circle(4,-6,0.09),
circle(4,-6,0.07),circle(4,-6,0.05),circle(4,-6,0.03),circle(4,-6,0.01),


circle(-3,-6,0.15),circle(-3,-6,0.13),circle(-3,-6,0.11),
circle(-3,-6,0.09),circle(-3,-6,0.07),circle(-3,-6,0.05),
circle(-3,-6,0.03),circle(-3,-6,0.01),

circle(-1,4,0.15),circle(-1,4,0.13),circle(-1,4,0.11),circle(-1,4,0.09),
circle(-1,4,0.07),circle(-1,4,0.05),circle(-1,4,0.03),circle(-1,4,0.01),

circle(1,6,0.15),circle(1,6,0.13),circle(1,6,0.11),circle(1,6,0.09),
circle(1,6,0.07),circle(1,6,0.05),circle(1,6,0.03),circle(1,6,0.01),

circle(2,4,0.15),circle(2,4,0.13),circle(2,4,0.11),circle(2,4,0.09),
circle(2,4,0.07),circle(2,4,0.05),circle(2,4,0.03),circle(2,4,0.01) )}}}

Edwin</pre>