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Which of the following functions is equivalent to the one shown below? v= - 4x2 + 56x-194 O A. y - 194 = - 4(x + 7)? O B. y-2= - 4(x-7)2 - O c. y = - 4x(x - 14) O d.y= - (2x + 4)(2x +48)

Which Of The Following Functions Is Equivalent To The One Shown Below V 4x2 56x194 O A Y 194 4x 7 O B Y2 4x72 O C Y 4xx 14 O Dy 2x 42x 48 class=

Answer :

Given:

The function is,

[tex]y=-4x^2+56x-194[/tex]

Explanation:

Simplify the equation.

[tex]\begin{gathered} y=-4x^2+56x-194 \\ y=-4x^2+56x-196+2 \\ y-2=-4x^2+56x-196 \end{gathered}[/tex]

Factorise the equation.

[tex]\begin{gathered} y-2=-4(x^2-14x+49) \\ y-2=-4(x^2-7x-7x+49) \\ y-2=-4\lbrack x(x-7)-7(x-7)\rbrack \\ y-2=-4(x-7)(x-7) \\ y-2=-4(x-7)^2 \end{gathered}[/tex]

So option B is correct.

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