Determine the vertex of the graph of the quadratic function
$f ( x ) = x ^ { 2 } + 5 x + \frac { 29 } { 4 }$.

A) $\left( \frac { - 5 } { 2 } , \frac { 27 } { 2 } \right)$

B) $\left( 5 , \frac { 29 } { 4 } \right)$

C) $\left( \frac { 5 } { 2 } , \frac { 29 } { 4 } \right)$

D) $\left( \frac { 5 } { 4 } , \frac { 21 } { 4 } \right)$

E) $\left( \frac { - 5 } { 2 } , 1 \right)$

Question

Determine the vertex of the graph of the quadratic function 
$f ( x ) = x ^ { 2 } + 5 x + \frac { 29 } { 4 }$.

A) $\left( \frac { - 5 } { 2 } , \frac { 27 } { 2 } \right)$

B) $\left( 5 , \frac { 29 } { 4 } \right)$

C) $\left( \frac { 5 } { 2 } , \frac { 29 } { 4 } \right)$

D) $\left( \frac { 5 } { 4 } , \frac { 21 } { 4 } \right)$

E) $\left( \frac { - 5 } { 2 } , 1 \right)$

Quizplus · Accepted Answer

The vertex form of a quadratic function is $f(x) = a(x-h)^2 + k$, where $(h, k)$ is the vertex. For $f(x) = x^2 + 5x + \frac{29}{4}$, the vertex $x$-coordinate is $-\frac{b}{2a} = -\frac{5}{2}$. Substituting $x = -\frac{5}{2}$ into the function gives the $y$-coordinate as 1, so the vertex is $\left( \frac{-5}{2}, 1 \right)$.

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 $f ( x ) = x ^ { 2 } + 5 x + \frac { 29 } { 4 }$