Answer:
1) [tex](x,y) = (0,-27)[/tex], 2) [tex]V(x,y) = (3, -36)[/tex].
Step-by-step explanation:
1) The ordered pair of the parabola is:
[tex]f(0) = 0^{2} - 6\cdot (0) -27[/tex]
[tex]f(0) = -27[/tex]
[tex](x,y) = (0,-27)[/tex]
2) The quadratic function needs to be rearranged into the standard form:
[tex]y = x^{2}-6\cdot x -27[/tex]
[tex]y = x^{2} - 6\cdot x + 9 -9 -27[/tex]
[tex]y = (x-3)^{2}-36[/tex]
[tex]y + 36 = (x-3)^{2}[/tex]
The vertex is [tex]V(x,y) = (3, -36)[/tex].
