Question

VERTEX FORM The vertex form of a quadratic function is \(y=a(x-h)^{2}+k\). Its graph is a parabola with vertex at \((\boldsymbol{h}, \boldsymbol{k})\). Use completing the square to write the quadratic function in vertex form. Then give the coordinates of the vertex of the graph of the function. $$y=x^{2}+10 x+25$$

Short answer

The vertex form of the function is \(y=(x-5)^{2}\) and the vertex of the parabola is at the point (5, 0).

Step-by-step solution

Rewrite in vertex form

The given equation is already in the vertex form \(y=(x-5)^{2}+0\). The term \(x^{2}+10x+25\) can be written as \((x-5)^{2}\), hence there is no need of completing the square.

Find the vertex

From the vertex form of the equation, we can see that the vertex is at \((h, k)\), hence the vertex for the given equation is at \((5, 0)\).