Question

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

Answer 1

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)

Answer 2

Answer:

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

Step-by-step 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).