Question

Rewrite each equation in the vertex form by completing the square. Then identify the vertex.

Answer 1

`y = { x }^(2) - 10x + 22 \\ = {x}^(2) - 10x + 25 - 3 \\ = {(x - 5)}^(2) - 3 \\ V:(5, - 3)`

Answer 2

Vertex of equation is (5,-3).

Explanation:

We have given a quadratic equation in standard form.

y = x²-10x+22

We have to rewrite given equation in vertex form.

y = (x-h)²+k is vertex form of equation where (h,k) is vertex of equation.

We will use method of completing square to solve this.

Adding and subtracting (-5)² to above equation, we have

y = x²-10x+22+(-5)²-(-5)²

y = x²-10x+(-5)²+22-(-5)²

y = (x-5)²+22-25

y = (x-5)²-3

Hence, vertex of equation is (5,-3).