Question

Rewrite y = x2 +6x+ 10 in graphing (vertex) form by completing the square. State the VERTEX.

Answer 1

The vertex of the graph is (-3,1)

Explanation:

Here, we want to rewrite the given quadratic equation in the vertex form

We have the vertex form as;

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

where the vertex is (h,k)

Now, by completing the square, we have to divide the coefficient of x by 2, then square; after which we add to both sides; prior to this, we have to replace y by 0

Thus, we have it as follows;

x^2 + 6x + 10 = 0

x^2 + 6x + 10 + 3^2 = 3^2

x^2 + 6x + 19 = 9

x^2 + 6x + 9 = 9-10

(x + 3)^2 = -1

(x + 3)^2 + 1 = 0

So we have the vertex as ;

(h,k) = (-3,1)