Question 866114
the vertex of a parabola is it (-4,-3). If one x-intercept is -11, what is the other x-intercept
<pre>
We plot those two points

{{{drawing(400,240,-14,6,-6,6, graph(400,240,-14,6,-6,6),

circle(-11,0,0.15),circle(-11,0,0.13),circle(-11,0,0.11),circle(-11,0,0.09),circle(-11,0,0.07),circle(-11,0,0.05),circle(-11,0,0.03),circle(-11,0,0.01),





circle(-4,-3,0.15),circle(-4,-3,0.13),circle(-4,-3,0.11),circle(-4,-3,0.09),circle(-4,-3,0.07),circle(-4,-3,0.05),circle(-4,-3,0.03),circle(-4,-3,0.01)

)}}}

The parabola's axis of symmetry is a vertical line thgrough the vertex,
so we draw in the axis of symmetry (in green)

{{{drawing(400,240,-14,6,-6,6, graph(400,240,-14,6,-6,6),

circle(-11,0,0.15),circle(-11,0,0.13),circle(-11,0,0.11),circle(-11,0,0.09),circle(-11,0,0.07),circle(-11,0,0.05),circle(-11,0,0.03),circle(-11,0,0.01),

green(line(-4,10,-4,-10)),



circle(-4,-3,0.15),circle(-4,-3,0.13),circle(-4,-3,0.11),circle(-4,-3,0.09),circle(-4,-3,0.07),circle(-4,-3,0.05),circle(-4,-3,0.03),circle(-4,-3,0.01)

)}}}





Now we sketch the parabola

{{{drawing(400,240,-14,6,-6,6, graph(400,240,-14,6,-6,6,(3/49)(x+4)^2-3),

circle(-11,0,0.15),circle(-11,0,0.13),circle(-11,0,0.11),circle(-11,0,0.09),circle(-11,0,0.07),circle(-11,0,0.05),circle(-11,0,0.03),circle(-11,0,0.01),

red(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)),


green(line(-4,10,-4,-10)),


circle(-4,-3,0.15),circle(-4,-3,0.13),circle(-4,-3,0.11),circle(-4,-3,0.09),circle(-4,-3,0.07),circle(-4,-3,0.05),circle(-4,-3,0.03),circle(-4,-3,0.01)

)}}}

We can see by the symmetry of a parabola that the other x-intercept
must be the same distance on the right of -4 (since that's the 
x-coordinate of the vertex), as (-11,0) is to the left of -4.  Since
-11 is 7 units to the left of -4, the x-intercept must be 7 units to
the right of -4 on the x-axis.  And -4+7 = 3.  So the other x-intercept
is (3,0),

Edwin</pre>