Find the vertex of $f ( x ) = 2 x ^ { 2 } - 3 x - 4$ .
A) $\left( \frac { 3 } { 4 } , - \frac { 41 } { 8 } \right)$
B) $\left( - \frac { 3 } { 4 } , - \frac { 5 } { 8 } \right)$
C) $\left( \frac { 3 } { 4 } , - \frac { 5 } { 8 } \right)$
D) $\left( - \frac { 3 } { 4 } , \frac { 41 } { 8 } \right)$

Question

Quizplus · Accepted Answer

The vertex of a parabola given by $f(x) = ax^2 + bx + c$ can be found using the formula $\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)$. For $f(x) = 2x^2 - 3x - 4$, $a = 2$, $b = -3$, and $c = -4$. Thus, the x-coordinate of the vertex is $-\frac{-3}{2*2} = \frac{3}{4}$. Substituting $x = \frac{3}{4}$ into $f(x)$ gives the y-coordinate: $2\left(\frac{3}{4}\right)^2 - 3\left(\frac{3}{4}\right) - 4 = -\frac{41}{8}$. Therefore, the vertex is $\left(\frac{3}{4}, -\frac{41}{8}\right)$.

Find the Vertex Of f(x)=2x2−3x−4f ( x ) = 2 x ^ { 2 } - 3 x - 4f(x)=2x2−3x−4

Find the Vertex Of $f ( x ) = 2 x ^ { 2 } - 3 x - 4$