Find the vertex of the graph of the function $y = 9 x ^ { 2 } + 6 x + 4$ by using the formula $x = - b / ( 2 a )$ .
A) $( 24,5,332 )$
B) $\left( - \frac { 1 } { 3 } , 3 \right)$
C) $\left( \frac { 1 } { 3 } , 7 \right)$
D) $( - 24,5,044 )$
E) $\left( - \frac { 1 } { 3 } , 7 \right)$

Question

Quizplus · Accepted Answer

The vertex of a parabola given by $y = ax^2 + bx + c$ can be found using the formula $x = -\frac{b}{2a}$. For the given function $y = 9x^2 + 6x + 4$, $a = 9$ and $b = 6$, so $x = -\frac{6}{2*9} = -\frac{6}{18} = -\frac{1}{3}$. Substituting $x = -\frac{1}{3}$ into the original equation gives $y = 9(-\frac{1}{3})^2 + 6(-\frac{1}{3}) + 4 = 3$. Therefore, the vertex is $\left( -\frac{1}{3}, 3 \right)$.

Find the Vertex of the Graph of the Function y=9x2+6x+4y = 9 x ^ { 2 } + 6 x + 4y=9x2+6x+4

Find the Vertex of the Graph of the Function $y = 9 x ^ { 2 } + 6 x + 4$