Posted by Erica on Saturday, August 2, 2008 at 9:12am.
The standard form is
ax^2 + bc + c = 0
The value of ax^2 + bx +c will be zero when
x = [-b +/- sqrt (b^2-4ac)]/2a
If you want to write a quadratic equation that is zero at given values x=d and x=e, first write it as
(x-d)(x-e) = 0
and then multiply it out for the standard form:
x^2 -(d+e)x + de = 0
say you had (4,0) and (-3,0) given as zeros of a quadratic function.
Then x-4 = 0
plus x+3 = 0
and
(x-4)(x+3) = 0
and
x^2 - x - 12 = 0
I suppose I could generalize that to zeros at a and b
x-a = 0
x-b = 0
so
(x-a)(x-b) = 0
x^2 -(a+b)x + a b = 0
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