Determine the vertex of the graph of the quadratic function $f ( x ) = x ^ { 2 } + 5 x + \frac { 29 } { 4 }$ .
A) $\left( \frac { 5 } { 2 } , \frac { 29 } { 4 } \right)$
B) $\left( \frac { 5 } { 4 } , \frac { 21 } { 4 } \right)$
C) $\left( - \frac { 5 } { 2 } , 1 \right)$
D) $\left( - \frac { 5 } { 2 } , \frac { 27 } { 2 } \right)$
E) $\left( 5 , \frac { 29 } { 4 } \right)$

Question

Determine the vertex of the graph of the quadratic function $f ( x ) = x ^ { 2 } + 5 x + \frac { 29 } { 4 }$ .
A) $\left( \frac { 5 } { 2 } , \frac { 29 } { 4 } \right)$
B) $\left( \frac { 5 } { 4 } , \frac { 21 } { 4 } \right)$
C) $\left( - \frac { 5 } { 2 } , 1 \right)$  
D) $\left( - \frac { 5 } { 2 } , \frac { 27 } { 2 } \right)$
E) $\left( 5 , \frac { 29 } { 4 } \right)$

Quizplus · Accepted Answer

The vertex of a quadratic function $f(x) = ax^2 + bx + c$ is given by $(- \frac{b}{2a}, f(- \frac{b}{2a}))$. For $f(x) = x^2 + 5x + \frac{29}{4}$, $a = 1$, $b = 5$, so the x-coordinate of the vertex is $- \frac{5}{2(1)} = - \frac{5}{2}$. Substituting $- \frac{5}{2}$ into $f(x)$ gives the y-coordinate as $1$, making the vertex $\left( - \frac{5}{2}, 1 \right)$.

Determine the Vertex of the Graph of the Quadratic Function f(x)=x2+5x+294f ( x ) = x ^ { 2 } + 5 x + \frac { 29 } { 4 }f(x)=x2+5x+429​

Determine the Vertex of the Graph of the Quadratic Function $f ( x ) = x ^ { 2 } + 5 x + \frac { 29 } { 4 }$