Question

find the vertex of the graph of the quadratic function. determine whether the graph opens upward or downward, find any intercepts, and sketch the graph.
$f(x) = 2x^2 + 8x + 14$
the vertex is
(simplify your answer. type an ordered pair.)

Explanation:

Step1: Recall vertex formula for quadratic

For a quadratic function \( f(x) = ax^2 + bx + c \), the x - coordinate of the vertex is given by \( x = -\frac{b}{2a} \). Here, \( a = 2 \), \( b = 8 \).
\( x = -\frac{8}{2\times2} = -2 \)

Step2: Find y - coordinate of vertex

Substitute \( x = -2 \) into \( f(x)=2x^{2}+8x + 14 \).
\( f(-2)=2\times(-2)^{2}+8\times(-2)+14 \)
\( = 2\times4-16 + 14 \)
\( = 8-16 + 14 \)
\( = 6 \)

Answer:

\((-2,6)\)