Question

Paul must find the zeros of the function f ( x ) = 4 x 2 − 56 x + 192 . To do so, he factors the quadratic function. Which function is equivalent to f(x) and reveals the zeros of the function? A. f ( x ) = ( 4 x − 48 ) ( x − 4 ) B. f ( x ) = 4 ( x − 48 ) ( x − 4 ) C. f ( x ) = ( 4 x − 6 ) ( x − 8 ) D. f ( x ) = 4 ( x − 6 ) ( x − 8 )

Answer 1

Explanation:

The function f(x) = 4x^2-56x+192.

We can first factor out a 4 from each term in the equation to get 4(x^2-14x+48).

Now, a quadratic equation looks like ax^2+bx+c. a=1, b=-14, and c=48.

The two values of x that give us zeros, we can set them equal to b and c such that:

x1+x2 = -14

x1*x2 = 48.

These two values will be x1=-6 and x2=-8, as -6-8=14 and -6*-8 = 48.

Thus we can factor 4(x^2-14x+48) out to get 4(x-6)(x-8).

So in summary, 4x^2-56x+192 = 4(x-6)(x-8) which is answer D.

Hope that helps!