Asked by hi
Use factoring to find the x intercepts of the graphs of these quadratic poly-nomials:y=ax2+bx+c,where a,b,c are constants
Answers
Answered by
hi
the quadratic polynomial is y = ax^2+bx+c
Answered by
Damon
a x^2 + b x = 0 - c
x^2 + (b/a) x + b^2 / 4a^2 = - c/a + b^2/ 4a^2
now factor
(x + b / 2a )^2 = - 4ac / 4 a^2 + b^2 / 4a^2
x + b/2a = +/- sqrt [ (b^2-4ac) / 4a^2 ]
x = -b/2a +/- sqrt(b^2-4ac) /2a
x = [ -b +/- sqrt (b^2 - 4 ac ) ] / 2a
look familiar?
x^2 + (b/a) x + b^2 / 4a^2 = - c/a + b^2/ 4a^2
now factor
(x + b / 2a )^2 = - 4ac / 4 a^2 + b^2 / 4a^2
x + b/2a = +/- sqrt [ (b^2-4ac) / 4a^2 ]
x = -b/2a +/- sqrt(b^2-4ac) /2a
x = [ -b +/- sqrt (b^2 - 4 ac ) ] / 2a
look familiar?
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