Identify the vertex, axis of symmetry, and intercepts for the graph of the function.
-$$y = x ^ { 2 } + 8 x + 14$$
A) Vertex at $( - 4 , - 2 )$; axis: $y = - 2 ; x$-intercepts: none; $y$-intercept: $( - 4 - \sqrt { 2 } , 0 )$
B) Vertex at $( - 4 , - 2 )$; axis: $x = - 4 ; x$-intercepts: $( - 4 - \sqrt { 2 } , 0 )$ and $( - 4 + \sqrt { 2 } , 0 ) ; y$-intercept: $( 0,14 )$
C) Vertex at $( 4,62 )$; axis: $x = 4 ; x$-intercepts: none; $y$-intercept: $( - 4 + \sqrt { 2 } , 0 )$
D) Vertex at $( 4,62 )$; axis: $y = 62 ; x$-intercepts: $( - 4 - \sqrt { 2 } , 0 )$ and $( - 4 + \sqrt { 2 } , 0 ) ; y$-intercept: $( 0,14 )$

Question

Quizplus · Accepted Answer

The vertex of a parabola in the form $y = ax^2 + bx + c$ can be found using the formula $(-b/2a, f(-b/2a))$. For $y = x^2 + 8x + 14$, the vertex is at $(-4, -2)$. The axis of symmetry is a vertical line through the vertex, hence $x = -4$. The $y$-intercept is found by setting $x = 0$, giving $y = 14$. The $x$-intercepts are found by solving $x^2 + 8x + 14 = 0$, which yields $x = -4 \pm \sqrt{2}$.

Identify the Vertex, Axis of Symmetry, and Intercepts for the Graph