QUESTIONS - ANGELA - CONICS

QUESTIONS/ANSWERS
CONICS

On 10/30/06, Angela <noreply-comment@blogger.com> wrote:

> Angela has left a new comment on your post "PANCHATANTRA - 5.COMMUNICATION":
>
> Determine the vertex of the function f(x)= x^2+2x-3

F(X)=[X^2+2*X*1+1]-1-3=(X+1)^2-4
HENCE VERTEX IS AT X+1=0...OR...X=-1...THEN ..F(X) =-4
SINCE (X+1)^2 IS ALWAYS GREATER THAN OR EQUAL TO ZERO,WE HAVE A MINIMUM
VALUE OF F(X)=-4 AT THE VERTEX.(1,-4)

Does the graph of the
> function open up or down?

UP
Why?
BECAUSE THE VERTEX IS A MINIMUM.

Determine the range of the function above.

at x=-1 ,the function has a minimum of -4 as x tends to minus or plus
infinity , the function tends to plus infinity.
hence range is -4 to infinity.....(-4,infinity)

On
> what intervals is the function above increasing or decreasing? Use set
> notation.

the function has a minimum at x =-1
> hence from x=-infinity to -1 the function decreases ..
x =(-infinity,-1)
and
increases from x= -1 to plus infinity...(-1,infinity)