Write the quadratic function $f ( x ) = x ^ { 2 } + 2 x + 5$ in standard form.
A) $f ( x ) = - ( x + 1 ) ^ { 2 } - 4$
B) $f ( x ) = ( x - 4 ) ^ { 2 } - 1$
C) $f ( x ) = - ( x - 1 ) ^ { 2 } - 4$
D) $f ( x ) = ( x + 1 ) ^ { 2 } + 4$
E) $f ( x ) = - ( x - 4 ) ^ { 2 } + 1$

Question

Quizplus · Accepted Answer

The standard form of a quadratic function is $f(x) = a(x - h)^2 + k$, where $(h, k)$ is the vertex of the parabola. Completing the square for $f(x) = x^2 + 2x + 5$, we add and subtract $(\frac{2}{2})^2 = 1$ inside the function: $f(x) = (x^2 + 2x + 1) + 5 - 1 = (x + 1)^2 + 4$, which matches option D.

Write the Quadratic Function f(x)=x2+2x+5f ( x ) = x ^ { 2 } + 2 x + 5f(x)=x2+2x+5

Write the Quadratic Function $f ( x ) = x ^ { 2 } + 2 x + 5$