Find the vertex of the graph of the quadratic function.
-$f ( x ) = x ^ { 2 } + x + 5$
A) $( - 1,5 )$
B) $\left( - \frac { 1 } { 2 } , \frac { 19 } { 4 } \right)$
C) $\left( \frac { 1 } { 2 } , \frac { 23 } { 4 } \right)$
D) $( 1,7 )$

Question

Quizplus · Accepted Answer

The vertex of a quadratic function in the form $f(x) = ax^2 + bx + c$ can be found using the formula $(- \frac{b}{2a}, f(- \frac{b}{2a}))$. For $f(x) = x^2 + x + 5$, $a = 1$, $b = 1$, so the x-coordinate of the vertex is $- \frac{1}{2}$. Plugging this back into the function gives $f(- \frac{1}{2}) = (- \frac{1}{2})^2 + (- \frac{1}{2}) + 5 = \frac{1}{4} - \frac{1}{2} + 5 = \frac{19}{4}$, making the vertex $\left( - \frac{1}{2}, \frac{19}{4} \right)$.

Find the Vertex of the Graph of the Quadratic Function f(x)=x2+x+5f ( x ) = x ^ { 2 } + x + 5f(x)=x2+x+5

Find the Vertex of the Graph of the Quadratic Function $f ( x ) = x ^ { 2 } + x + 5$