SOLUTION: 20. 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)=x^2-2x-5

Algebra ->  Equations -> SOLUTION: 20. 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)=x^2-2x-5      Log On


   

Question 1157013: 20.
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)=x^2-2x-5
Found 2 solutions by josgarithmetic, Boreal:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=x%5E2-2x-5
You already see f contains a point (0,-5).

Try completing the square.
x%5E2-2x%2B1-5-1
%28x%5E2-2x%2B1%29-6
%28x-1%29%5E2-6
Vertex is (1,-6).

Directrix:
4p=1, the lead coefficient
p=1%2F4, distance of vertex from either focus or directrix
-
y=-1%2F4----------the Directrix


graph%28400%2C400%2C-10%2C10%2C-10%2C10%2Cx%5E2-2x-5%29

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
the vertex x point is at -b/2a and b is -2 and a is the coefficient of x or 1
so the vertex x point is +1
f(1)=1-2-5=-6
so the vertex is at (1, -6)
The axis of symmetry is the x-value or x=1
for 5 points,
first pick x=0, and f(0)=-5. that is easy
the vertex is a point, so you have that.
Try -1 and you get 1+2-5=-2
try 2 and you get -5
because -1 is two units away from 1, and +3 is two units away from 1, and the function is symmetrical, the y-values are the same. So f(-1)=f(3)=-2
if you look at f(-2) three units from the axis, f(4) is also 3 units away, and they have the same y-value.

graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E2-2x-5%29