# Vertex of a Parabola

### Example 1

Find the vertex of $y=x^2 + 4x +2$.

\begin{align} \displaystyle y &= x^2 + 4x +2 \\ &= x^2 + 4x + 4-2\\ &= (x+2)^2-2 \\ \therefore &(-2,-2) \end{align}

### Example 2

Find the vertex of $y=x^2 – 6x +1$.

\begin{align} \displaystyle y &= x^2-6x +1 \\ &= x^2-6x + 9 +8 \\ &= (x-3)^2 +8 \\ \therefore &(3,8) \end{align}

### Example 3

Find the vertex of $y= -x^2 + 4x +1$.

\begin{align} \displaystyle y &= -(x^2-4x) + 1 \\ &= -(x^2-4x + 4) + 4 + 1 \\ &= (x-2)^2+5 \\ \therefore &(2,5) \end{align}

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