SOLUTION: 16. I need help graphing the following and listing the directions, vertex, axis of symmetry,table with 5 points and the graph for this equation f(x)= -1/3(x-1)^2-2

Algebra ->  Equations -> SOLUTION: 16. I need help graphing the following and listing the directions, vertex, axis of symmetry,table with 5 points and the graph for this equation f(x)= -1/3(x-1)^2-2      Log On


   

Question 1157009: 16.
I need help graphing the following and listing the directions, vertex, axis of symmetry,table with 5 points and the graph for this equation
f(x)= -1/3(x-1)^2-2
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=+-%281%2F3%29%28x-1%29%5E2-2
compare to F%28x%29=+a%28x-h%29%5E2%2Bk
from given formula you see that h=1 and k=-2, so vertex is at (1,-2)
the vertical line that goes through the vertex
x=+1
directrix:
y=+-%281%2F3%29%28x-1%29%5E2-2
y%2B2=+-%281%2F3%29%28x-1%29%5E2
%28y%2B2%29%2F%28-1%2F3%29=+%28x-1%29%5E2
-3%28y%2B2%29%29=+%28x-1%29%5E2.........compare to 4p%28y-k%29=%28h-h%29%5E2
you see that 4p=-3=>p=-3%2F4
y=-2-%28-3%2F4%29
y=-8%2F4%2B3%2F4
y=-5%2F4
table:
x|y
1|-2
-1|-10%2F3...y=+-%281%2F3%29%28-1-1%29%5E2-2=-10%2F3
2|-7%2F3...y=+-%281%2F3%29%282-1%29%5E2-2=-7%2F3
0|-7%2F3...y=+-%281%2F3%29%280-1%29%5E2-2=-7%2F3
-2|-5...y=+-%281%2F3%29%28-2-1%29%5E2-2=-5