Question 355143
Hi,

g(x)=x^2-6x+5
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Factoring to find the intercepts
g(x)=x^2-6x+5 = (x - 5)(x - 1)
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Intercepts (5,0) and (1, 0)
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*Note: Complete the square to put into the vertex form of an equation of a parabola y = a(x - h)^2 + k where (h,k) is the vertex
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(completing the square by adding and subtracting 9)

g(x) = x^2-6x+5 = (x^2 - 6x + 9) -9 + 5= (x-3)^2 -4

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vertex = (3, -4) this is the minimum 
(a = 1, parabola opens upward)
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Range is ({{{-4}}},{{{infinity}}})
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{{{ graph( 300, 200,-6,6,-6,6,x^2-6x +5) }}}