Find the Vertex y=x^2+6x+9

Problem

y=x2+6*x+9

Solution

1. Identify the coefficients of the quadratic equation in the form y=a*x2+b*x+c where a=1 b=6 and c=9

2. Calculate the x-coordinate of the vertex using the formula x=−b/(2*a)

x=−6/(2*(1))

x=−3

3. Substitute the x-coordinate back into the original equation to find the y-coordinate.

y=(−3)2+6*(−3)+9

y=9−18+9

y=0

4. State the vertex as the ordered pair (x,y)

Final Answer

Vertex=(−3,0)

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