Find the Vertex y=x^2+2x+5

Problem

y=x2+2*x+5

Solution

1. Identify the coefficients of the quadratic equation in the form y=a*x2+b*x+c where a=1 b=2 and c=5

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

x=−2/(2*(1))

x=−1

3. Substitute the xcoordinate back into the original equation to find the ycoordinate.

y=(−1)2+2*(−1)+5

4. Simplify the expression to determine the value of y

y=1−2+5

y=4

Final Answer

Vertex=(−1,4)

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