Respuesta :

kudzordzifrancis

ANSWER

Vertex form:

[tex]y = 2( {x - 4)}^{2} - 27[/tex]

Vertex:

V(4,-27)

EXPLANATION

The given function is

[tex]y = 2 {x}^{2} - 16x + 5[/tex]

Complete the square as follows:

[tex]y = 2( {x}^{2} - 8x) + 5[/tex]

[tex]y = 2( {x}^{2} - 8x + 16) + 5 - 2 \times 16[/tex]

[tex]y = 2( {x - 4)}^{2} + 5 - 32[/tex]

The vertex form is:

[tex]y = 2( {x - 4)}^{2} - 27[/tex]

The vertex is:

V(4,-27)

zainebamir540

Answer:

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

Step-by-step 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).

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