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when discriminant is more than 0
two real roots
discriminant=0
1 repeated root (tangent)
discriminant is less than 0
no real roots
why must apparent solutions be rejected
domain widens when logs are combined
building a quadratic
when max/min point (h,k) is given= y=a(x-h)2+k
when x-intercepts are given (p+q)= y=a(x-p)(x-q)
when three general points are needed= y=ax2+bx+c
applied exponential equations
A=P(r+i)n
finding rate of change
15%/100=0.15 (increase-1+0.15, decrease 1-0.15)