Write the equation of the parabola in standard form and find the vertex of its graph. $y = x ^ { 2 } + 10 x + 16$
A) $y = ( x + 5 ) ^ { 2 } - 9$ ; vertex: $( 5 , - 41 )$
B) $y = ( x - 5 ) ^ { 2 } + 11$ ; vertex: $( 5,41 )$
C) $y = ( x + 8 ) ( x + 2 )$ ; vertex: $( 10,16 )$
D) $y = ( x + 5 ) ^ { 2 } - 9$ ; vertex: $( - 5 , - 9 )$
E) $y = ( x + 5 ) ^ { 2 } + 41$ ; vertex: $( - 5,41 )$

Question

Quizplus · Accepted Answer

To convert the given equation $y = x^2 + 10x + 16$ to its standard form, we complete the square. The equation can be rewritten as $y = (x^2 + 10x + 25) - 25 + 16$, which simplifies to $y = (x + 5)^2 - 9$. The vertex form of a parabola is $y = a(x - h)^2 + k$, where $(h, k)$ is the vertex. Thus, the vertex of the given parabola is $(-5, -9)$.

Write the Equation of the Parabola in Standard Form and Find