Question

find the vertex of each quadratic function by completing the square

Answer 1

We can see that

$(x+2)^2=x^2+4x+4$

By comparing this expression with our quadratic function, we get

$y\questeq x^2+4x+4-4-16$

where we added and substracted 4, which gives zero. Now, we can write

$\begin{gathered} y=(x+2)^2-4-16 \\ y=(x+2)^2-20 \end{gathered}$

Now, the quadratic function in vertex form is given by

$y=a(x+h)^2+k$

where the point (h,k) is the vertex. By comparing our last result and this expression, we can see that h=2 and k=-20. Then, the vertex is at point (2,-20).