Q: What is the vertex of x2 plus 18x plus 19?

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Y = X2 + 18X + 52 set to 0 X2 + 18X + 52 = 0 subtract 52 from each side X2 + 18X = - 52 now, halve the coefficient of the variable term (18), square it and add it to both sides X2 + 18X + 81 = - 52 + 81 now, factor on left and gather terms on right (X + 9)2 = 29 (X + 9)2 - 29 = 0 ---------------------------vertex form

x2-18x+81 = (x-9)(x-9) when factored

9x2 - 18x + 99(x2 - 2x + 1)==========

The vertex is at (-1,0).

(x+3)(x+15)

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Y = X2 + 18X + 52 set to 0 X2 + 18X + 52 = 0 subtract 52 from each side X2 + 18X = - 52 now, halve the coefficient of the variable term (18), square it and add it to both sides X2 + 18X + 81 = - 52 + 81 now, factor on left and gather terms on right (X + 9)2 = 29 (X + 9)2 - 29 = 0 ---------------------------vertex form

x2 + 18x - 50 does not have rational factors.

Yes!

x2-18x+81 = (x-9)(x-9) when factored

The vertex is at (-1,0).

9x2 - 18x + 99(x2 - 2x + 1)==========

(x+3)(x+15)

(X-9)2

(-4,-1)

3x3+15x2+18x = 3x(x2+5x+6) = 3x(x+2)(x+3)

x2 + 18x + 45 = (x + 15)(x + 3).

The vertex has a minimum value of (-4, -11)