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PLEASE HELP!

Angela was completing the square of the quadratic function in order to find the extreme value. Her work is shown below. x2 + 8x + 6 (x2 + 8x + ) + 6 What is the next step in the process, and what is the extreme value?

A: (x2 + 8x + 16) + 6 - 16; the extreme minimum is -10

B: (x2 + 8x + 16) + 6 + 16; the extreme minimum is 22

C: (x + 4)2 – 10; the extreme minimum is -10

D: (x + 4)2 + 22; the extreme minimum is 22

Respuesta :

lublana

Answer:

A

Step-by-step explanation:

We are given that a function

[tex]f(x)=x^2+8x+6[/tex]

We have to find the next step in the process and what is the extreme value .

By adding and subtracting 16  then we get

[tex]f(x)=(x^2+8x+16)+6-16[/tex]

[tex]f(x)=(x+4)^2-10[/tex]

By using the formula

[tex](a+b)^2=a^2+b^2+2ab[/tex]

The given function is the equation of parabola .

By comparing  with

[tex]y=(x-h)^2+k[/tex]

Where vertex=(h,k)

Vertex=(h,k)=(-4,-10)

Substitute x=-4

Then, we get

[tex]f(x)=-10[/tex]

Hence, the extreme minimum value of function =-10

Option A is true.

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