Answer
The first part of the graph is the parabolic function $4-x^2$ until the point (1,3), which cuts the x-axis at (-2,0). The second part of the graph is the parabolic function $x^2 +2x$ from the point (1,3) on through (2,8).
Work Step by Step
$F(1) = 4 - 1^2$
$F(1) = 4 - 1$
$F(1) = 3$
The first part will cut the x-axis at:
$4-x^2 = 0$
$x^2 = 4$
$x = \sqrt4$ or $x = -\sqrt4$
$x = 2$ or $x = -2$
So the first part of the graph will be the parabolic function $4-x^2$ until the point (1,3), which cuts the x-axis at (-2,0).
$ F(1) = 1^2 + 2 \times 1$
$ F(1) = 1 + 2$
$ F(1) = 3$
$ F(2) = 2^2 + 2 \times 2$
$ F(2) = 4 + 4$
$ F(2) = 8$
So the second part of the graph will be the parabolic function $x^2 +2x$ from the point (1,3) on through (2,8).
