Rewrite the quadratic function in standard form by completing the square.
-$$f ( x ) = x ^ { 2 } + 5 x + 2$$
A) $f ( x ) = \left( x + \frac { 5 } { 2 } \right) ^ { 2 } - \frac { 17 } { 4 }$
B) $f ( x ) = \left( x - \frac { 5 } { 2 } \right) ^ { 2 } + \frac { 17 } { 4 }$
C) $f ( x ) = ( x - 5 ) ^ { 2 } + 23$
D) $f ( x ) = ( x + 5 ) ^ { 2 } - 23$

Question

Quizplus · Accepted Answer

To complete the square for the quadratic function $f(x) = x^2 + 5x + 2$, we first factor out the coefficient of $x^2$ (which is 1 in this case, so no change is needed). Then, we add and subtract the square of half the coefficient of $x$, which is $\left(\frac{5}{2}\right)^2 = \frac{25}{4}$. This gives us $f(x) = x^2 + 5x + \frac{25}{4} - \frac{25}{4} + 2$. Rearranging, we get $f(x) = \left(x + \frac{5}{2}\right)^2 - \frac{25}{4} + 2 = \left(x + \frac{5}{2}\right)^2 - \frac{17}{4}$, which matches choice A.

Rewrite the Quadratic Function in Standard Form by Completing the Square