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quADraTiC

ax^2+bx+c

turnin point

(-b/2a,-D/4a)

if a>0

parabola(katora)

turnin upward

a<0

parabola(curve) turnin downwards

if parabola is turnin upward then we find d least value of x,y

if katora turnin downwards then we finda highest value of x,y

if imaginary roots den d katora do nt cut x axis

a*f(k)<0

then k is 2 b betwn d roots

if a*f(k0>0

then k is 2 b outside

n if k>-b/2a

then k is 2 d right of d roots

if k<-b/2a

then k is 2 d left of d roots

f(k1)*f(k2)<0

means they trap only one root

if k<-b/2a

then they trap d samllest root

if k>-b/2a means they trap d biggest root

in wavy curve method:

if itz >=0 then consider only positive block

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