Find the vertex of $y = 5 - 3 x - x ^ { 2 }$ .
A) $\left( - \frac { 3 } { 2 } , \frac { 4 } { 29 } \right)$
B) $\left( \frac { 2 } { 3 } , \frac { 4 } { 29 } \right)$
C) $\left( - \frac { 3 } { 2 } , \frac { 29 } { 4 } \right)$
D) $\left( \frac { 3 } { 2 } , \frac { 29 } { 4 } \right)$
E) $\left( - 3 , \frac { 29 } { 4 } \right)$

Question

Find the vertex of  $y = 5 - 3 x - x ^ { 2 }$ .
A) $\left( - \frac { 3 } { 2 } , \frac { 4 } { 29 } \right)$
B) $\left( \frac { 2 } { 3 } , \frac { 4 } { 29 } \right)$
C) $\left( - \frac { 3 } { 2 } , \frac { 29 } { 4 } \right)$
D) $\left( \frac { 3 } { 2 } , \frac { 29 } { 4 } \right)$
E) $\left( - 3 , \frac { 29 } { 4 } \right)$

Quizplus · Accepted Answer

The vertex of a parabola in the form $y = ax^2 + bx + c$ can be found using the formula $(-b/2a, f(-b/2a))$. For $y = -x^2 - 3x + 5$, $a = -1$, $b = -3$, and $c = 5$. Thus, the x-coordinate of the vertex is $-(-3)/(2*(-1)) = 3/2$. Substituting $x = 3/2$ into the original equation gives the y-coordinate, which calculates to $29/4$. Therefore, the vertex is $\left( \frac { 3 } { 2 } , \frac { 29 } { 4 } \right)$.

Find the Vertex Of y=5−3x−x2y = 5 - 3 x - x ^ { 2 }y=5−3x−x2

Find the Vertex Of $y = 5 - 3 x - x ^ { 2 }$