f(x) = (x^2 - 6x ) + 1

f(x) = (x^2 - 6x + 9 ) + 1 - 9

f(x) = (x - 3)2 - 8

f(x) = a(x-h)2 + k

Vertex = (3, -8)

Axis of symmetry => x = 3

You could use -b/(2a), which gives you -(-6)/(2*1) = 3

f(3) = 3^2 - 6(3) + 1 = 9 - 18 + 1 = -8

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f(x) = x^2 - 6x + 1

f(x) = (x^2 - 6x ) + 1

f(x) = (x^2 - 6x + 9 ) + 1 - 9

f(x) = (x - 3)2 - 8

f(x) = a(x-h)2 + k

Vertex = (3, -8)

Axis of symmetry => x = 3

You could use -b/(2a), which gives you -(-6)/(2*1) = 3

f(3) = 3^2 - 6(3) + 1 = 9 - 18 + 1 = -8

f(x) = (x^2 - 6x ) + 1

f(x) = (x^2 - 6x + 9 ) + 1 - 9

f(x) = (x - 3)2 - 8

f(x) = a(x-h)2 + k

Vertex = (3, -8)

Axis of symmetry => x = 3

You could use -b/(2a), which gives you -(-6)/(2*1) = 3

f(3) = 3^2 - 6(3) + 1 = 9 - 18 + 1 = -8

The graph crosses the x axis in two places:

6 +/- sqrt(36-4)

------------------

2

6 +/- sqrt(32)

---------------

2

6 +/- sqrt(16) sqrt(2)

------------------------

2

6 +/- 4 sqrt(2)

----------------

2

x = 3 +/- 2sqrt(2)

Parabola is open upward, with a vertex at (3, -8), crossing the x axis at (3-2sqrt(2), 0), and (3+2sqrt(2), 0).

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...

f ( x ) = X^{2 }- 6X + 1

= X^{2 } - 2 ( 6x/ 2) + 9 = - 1 + 9

( X- 3)^{2} = 8 , X = 3 ±2√2

Vertex : ( 3, 8)

General formula : ( -b/(2a) , ^{ } (b^{2} - 4ac) / 4a^{2 ) }

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