Define the axis of symmetry, vertex, focus and directrix for
1 answer:
Answer:
see attached
Step-by-step explanation:
The equation is in the form ...
4p(y -k) = (x -h)^2 . . . . . (h, k) is the vertex; p is the focus-vertex distance
Comparing this to your equation, we see ...
p = 4, (h, k) = (3, 4)
p > 0, so the parabola opens upward. The vertex is on the axis of symmetry. That axis has the equation x=x-coordinate of vertex. This tells you ...
vertex: (3, 4)
axis of symmetry: x = 3
focus: (3, 8) . . . . . 4 units up from vertex
directrix: y = 0 . . . horizontal line 4 units down from vertex
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Answer:
f(n) = f(n - 1) + 3
Step-by-step explanation:
Substitute to get the recursive formula.
OPTION 1: f(n) = f(n - 1) + 3
Substituting n = 1.
f(1) = f(1 - 1) + 3 = 0 + 3 = 3.
Substituting n = 2.
f(2) = f(2 - 1) + 3 = f(1) + 3 = 3 + 3 = 6.
Substituting n = 3.
f(3) = f(3 - 1) + 3 = f(2) + 3 = 6 + 3 = 9.
The numbers match the given sequence. So, we say the above recursive formula represents the sequence.
OPTION 2: f(n) = f(n - 1) + 2
Substituting n = 1
f(1) = f(0) + 2 3.
So, this is eliminated.
Similarly, OPTION 3 and OPTION 4 can be eliminated as well.