Question

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)

Answer 1

Given:

The function is,

`y=-4x^2+56x-194`

Step-by-step explanation:

Simplify the equation.

`\begin{gathered} y=-4x^2+56x-194 \\ y=-4x^2+56x-196+2 \\ y-2=-4x^2+56x-196 \end{gathered}`

Factorise the equation.

`\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}`

So option B is correct.