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

Quizplus · Accepted Answer

The vertex of a quadratic function in the form $f(x) = ax^2 + bx + c$ can be found using the formula $(-b/2a, f(-b/2a))$. For the given function $f(x) = x^2 + 5x + \frac{29}{4}$, $a = 1$ and $b = 5$, so the x-coordinate of the vertex is $-5/(2*1) = -5/2$. Plugging this back into the function gives the y-coordinate as $f(-5/2) = (-5/2)^2 + 5(-5/2) + \frac{29}{4} = \frac{25}{4} - \frac{25}{2} + \frac{29}{4} = 1$. Therefore, 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 $f ( x ) = x ^ { 2 } + 5 x + \frac { 29 } { 4 }$