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 f(x) = 2(x-4)²+(-27) where vertex is (4,-27).

Explanation:

We have given a quadratic equation in standard form.

y= 2x²-16x+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.

y = 2(x²-8x)+5

Adding and subtracting (-4)² to above equation, we have

y = 2(x²-8x+(-4)²)+5-2(-4)²

y = 2(x-4)²+5-2(16)

y = 2(x-4)²+ 5 -32

y = 2(x-4)²-27

Hence, The vertex form of the given equation is f(x) = 2(x-4)²+(-27) where vertex is (4,-27).

Answer 2

Vertex form:

`y = 2( {x - 4)}^(2) - 27`

Vertex:

V(4,-27)

EXPLANATION

The given function is

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

Complete the square as follows:

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

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

`y = 2( {x - 4)}^(2) + 5 - 32`

The vertex form is:

`y = 2( {x - 4)}^(2) - 27`

The vertex is:

V(4,-27)