Question

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

Answer 1

The vertex form of the given equation is y = (x+4)²-11 where vertex is (-4,-11).

Explanation:

We have given a quadratic equation in standard form.

y = x²+8x+5

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 (4)² to above equation, we have

y = x²+8x+5 +(4)²-(4)²

y = x²+8x+(4)²+5-(4)²

y = (x)²+2(x)(4)+(4)²+5-16

y = (x+4)²-11

Hence, the vertex form of the given equation is y = (x+4)²-11 where vertex is (-4,-11).

Answer 2

ANSWER

Vertex form:


`y = ( {x + 4)}^(2) - 11`

Vertex

V(-4,-11)

EXPLANATION

The given expression is


`y = {x}^(2) + 8x + 5`

We complete the square to get the vertex form.

Add and subtract half the square of the coefficient of x.


`y = {x}^(2) + 8x + 16 + 5 - 16`


`y = ( {x + 4)}^(2) - 11`

The vertex is

V(-4,-11)