Question 999340
the quadratic formula for solutions of x is
x = (-b + sqrt(b^2 - 4ac)) / 2a
x = (-b - sqrt(b^2 - 4ac)) / 2a
you are given the sqrt in order to calculate the discriminant
sqrt((-12)^2 - 4 * 9 * 3) = sqrt(144 - 108) = 6
x = (-(-12) + 6) / (2 * 9) = 18 / 18 = 1
x = (-(-12) -6) / (2 * 9) = 6 / 18 = 1/3
there are two solutions 1, 1/3 both are rational numbers which are real numbers
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f(x) = 9x^2 -12x +3
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here is the function's graph
{{{ graph( 300, 200, -6, 5, -10, 10, 9x^2 -12x +3) }}}