A quadratic function is defined by f(x)=x^2-8x-4 . Which expression also defines f and best reveals the maximum or minimum of the function? Select the correct choice. A (x-4)^2+20 B x(x-8)-4 C (x-4)^2+12 D (x-4)^2-20

To determine which expression also defines the quadratic function \( f(x) = x^2 - 8x - 4 \) and best reveals the maximum or minimum of the function, we need to complete the square.<br /><br />Starting with the given function:<br />\[ f(x) = x^2 - 8x - 4 \]<br /><br />First, we complete the square for the quadratic expression \( x^2 - 8x \):<br /><br />1. Take the coefficient of \( x \), which is \(-8\), divide it by 2, and square the result:<br /> \[ \left(\frac{-8}{2}\right)^2 = (-4)^2 = 16 \]<br /><br />2. Add and subtract this square inside the function:<br /> \[ f(x) = x^2 - 8x + 16 - 16 - 4 \]<br /> \[ f(x) = (x^2 - 8x + 16) - 20 \]<br /><br />3. Rewrite the quadratic expression as a perfect square:<br /> \[ f(x) = (x - 4)^2 - 20 \]<br /><br />Thus, the expression that also defines \( f(x) \) and best reveals the maximum or minimum of the function is:<br />\[ f(x) = (x - 4)^2 - 20 \]<br /><br />Therefore, the correct choice is:<br />D \((x-4)^{2}-20\)