Write the quadratic function $f ( x ) = \frac { 1 } { 4 } \left( x ^ { 2 } + 8 x - 20 \right)$ in standard form.
A) $f ( x ) = \frac { 1 } { 4 } ( x + 4 ) ^ { 2 } - 9$
B) $f ( x ) = \frac { 1 } { 4 } ( x - 9 ) ^ { 2 } + 4$
C) $f ( x ) = \frac { 1 } { 4 } ( x - 4 ) ^ { 2 } + 9$
D) $f ( x ) = - \frac { 1 } { 9 } ( x + 4 ) ^ { 2 } - 9$
E) $f ( x ) = - \frac { 1 } { 9 } ( x - 4 ) ^ { 2 } - 9$

Question

Quizplus · Accepted Answer

To convert the given quadratic function to standard form, complete the square inside the parentheses. The standard form is $f(x) = a(x - h)^2 + k$, where $(h, k)$ is the vertex of the parabola. Completing the square for $x^2 + 8x - 20$ involves adding and subtracting $(\frac{8}{2})^2 = 16$, leading to $\frac{1}{4}[(x^2 + 8x + 16) - 16 - 20]$, which simplifies to $\frac{1}{4}(x + 4)^2 - 9$.

Write the Quadratic Function f(x)=14(x2+8x−20)f ( x ) = \frac { 1 } { 4 } \left( x ^ { 2 } + 8 x - 20 \right)f(x)=41​(x2+8x−20)

Write the Quadratic Function $f ( x ) = \frac { 1 } { 4 } \left( x ^ { 2 } + 8 x - 20 \right)$