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What is an equivalent form of the function f(x) = -x2-8x-12 that reveals the zeroes of the function?
O A. f(x)=-(x+4)2+4
O B. f(x)=-(x-4)2+4
OC. f(x)=-(x+2)(x+6)
O D. f(x)=-(x-2)(x-6)

Respuesta :

Answer:

C

Step-by-step explanation:

Given

f(x) = - x² - 8x - 12 ← factor out - 1 from each term

     = - (x² + 8x + 12) ← factor the quadratic

    = - (x + 2)(x + 6) → C

deepakrai138

The correct option is C.  [tex]f(x)=-(x+2)(x+6)[/tex].

Given function is  [tex]f(x) = -x^2-8x-12[/tex].

Here, [tex]f(x)= -x^2-8x-12[/tex]

[tex]f(x)=-[x^{2} +8x+12][/tex]

By middle term split method, splitting the middle term of the quadratic equation, we get

[tex]f(x)=-[x^{2} +6x+2x+12]\\[/tex]

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

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

Hence the required equivalent form of [tex]f(x)[/tex] is [tex]-[(x+6) (x+2)][/tex]. .

For more details on Zeroes of quadratic equation follow the link:

https://brainly.com/question/4318614

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