SOLUTION: Please help me list the directions,vertex, axis of symmetry, table of 5 points, graph ? 1.F(x)= -1/2x^2 2.F(x)=2(x+1)^2-3

Algebra ->  Equations -> SOLUTION: Please help me list the directions,vertex, axis of symmetry, table of 5 points, graph ? 1.F(x)= -1/2x^2 2.F(x)=2(x+1)^2-3      Log On


   

Question 1157027: Please help me list the directions,vertex, axis of symmetry, table of 5 points, graph ?
1.F(x)= -1/2x^2
2.F(x)=2(x+1)^2-3
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
1.
F%28x%29=+-%281%2F2%29x%5E2
compare to F%28x%29=+a%28x-h%29%5E2%2Bk
from given formula you see that h=0 and k=0, so vertex is at (0,0)
the vertical line that goes through the vertex
x=+0
directrix:
y=0-%28-1%2F2%29
y=1%2F2
table:
x|y
0|0
1|-1%2F2
2|-2
4|-8
-2|-2





2.
F%28x%29=2%28x%2B1%29%5E2-3
compare to F%28x%29=+a%28x-h%29%5E2%2Bk
from given formula you see that h=-1 and k=-3, so vertex is at (-1,-3)
the vertical line that goes through the vertex
x=+-1
directrix:
y=+2%28x%2B1%29%5E2-3
%281%2F2%29%28y%2B3%29=+%28x%2B1%29%5E2...since 4p=1%2F2=>p=1%2F8
y=-3-p
y=-3-1%2F8
y=-25%2F8
table:
x|y
-1|-3
1|5
-3|5
0|-1
-2|-1