find the vertex form of the function then find each of the f

find the vertex form of the function. then find each of the following. A) intercepts b) vertex c) maximum or minimum d) range

Solution

s(x)=-2x^2-4x+3

s(x)=-2(x^2-2x)+3

s(x)=-2(x^2-2x+1-1)+3

s(x)=-2(x^2-2x+1)+2+3

s(x)=-2(x-1)^2+3

A)

x=0, s(0)=-2*1+3=1

s=0,2(x-1)^2=3 , x-1=+-sqrt(3/2),x=1+-sqrt(3/2)

B)

s(x)-3=-2(x-1)^2

Vertex is: x=1,s=3

C)

-2(x-1)^2 is maximum at x=1 where it takes value 0

So , s maximum is:-2*0+3=3

There is no miniumum as as x gets larger: -2(x-1)^2 goes to -infinity

D)

Range is from minimum to -infinity

[3,-infinity)