SOLUTION: Please help me list the directions,vertex, axis of symmetry, table of 5 points, graph ? 1.F(x)= (x-6)^2+2 2. F(x) = x^2-2x-5

Algebra ->  Equations -> SOLUTION: Please help me list the directions,vertex, axis of symmetry, table of 5 points, graph ? 1.F(x)= (x-6)^2+2 2. F(x) = x^2-2x-5      Log On


   

Question 1157025: Please help me list the directions,vertex, axis of symmetry, table of 5 points, graph ?
1.F(x)= (x-6)^2+2
2. F(x) = x^2-2x-5
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
graphing the following and listing the directions,vertex,axis of symmetry,table with 5 points and the graph for this equation
f%28x%29=%28x-6%29%5E2%2B2
from given formula you see that h=6 and k=2, so vertex is at (6,2)
so, we have one point for a graph
For a parabola in standard form:y=ax%5E2%2Bbx%2Bc
the axis of symmetry is the vertical line that goes through the vertex
x=+-b%2F2a
in your case, x coordinate of the vertex is 6=:the vertical line that goes through the vertex
x=+6

directrix:
4p+%28y-k+%29=+%28x-h+%29%5E2 is the standard equation for an up-down facing parabola with vertex at (h, k+) and a focal length+abs%28p%29
Rewrite y=+%28x-6+%29%5E2%2B2 in the standard form:

4p%28y-2+%29=+%28x-6+%29%5E2.....since 4p=1=>p=1%2F4
y=2-p
y=2-1%2F4
y=8%2F4-1%2F4
y=7%2F4
table:
x|y
6|2
5|3
4|6
7|3
8|6


2.
F%28x%29+=+x%5E2-2x-5.....write in vertex form
F%28x%29+=+%28x%5E2-2x%2Bb%5E2%29-b%5E2-5
F%28x%29+=+%28x%5E2-2x%2B1%5E2%29-1%5E2-5
F%28x%29+=+%28x-1%29%5E2-6
vertex | (1, -6)
compare to4p+%28y-k+%29=+%28x-h+%29%5E2=>4p=1=>p=1%2F4
y=-6-p
y=-6-1%2F4
y=-25%2F4
directrix: y+=+-25%2F4
axis of symetry:the vertical line that goes through the vertex
x=+1
table:
x|y
1|-6
2|-5
3|-2
4|3
0|-5