Solution:
Given the graph;
(a) The domain of a function is the set of values for which the function is real and defined. Thus, the domain D is;
[tex]\begin{gathered} (-\infty,\infty) \\ D:All\text{ }real\text{ }numbers \end{gathered}[/tex]
The range is;
[tex]y\leq8[/tex]
The zeros of the function are the points y=0;
[tex]x=1,x=5[/tex]
(b) The equation of a parabola in vertex form is;
[tex]\begin{gathered} y=a(x-h)^2+k \\ Where\text{ }(h,k)\text{ is }the\text{ }vertex; \\ and\text{ }given\text{ }(1,0) \\ \\ 0=a(1-3)^2+8 \\ \\ -8=4a \\ \\ a=-2 \\ \\ \end{gathered}[/tex]
Thus, the equation is;
[tex]y=-2(x-3)^2+8[/tex]
(c) Using the graph below;
The graph of g(x) has its intercept at (0,0).
The transformation goes as;
Vertical stretch 2units, reflection over the x-axis, horizontal shift to the the right 3 units, vertical shift up 8 units
Using (5,0);
[tex]\begin{gathered} y=a(x-h)^2+k \\ \\ 0=a(5-3)^2+8 \\ 4a=-8 \\ \\ a=-2 \end{gathered}[/tex]
