Find the vertex and focus of the parabola. $y ^ { 2 } = - \frac { 3 } { 4 } x$
A)vertex: $\left( 0 , - \frac { 3 } { 4 } \right)$ focus: $\left( - \frac { 3 } { 4 } , - \frac { 3 } { 4 } \right)$
B)vertex: (0, 0) focus: $\left( 0 , - \frac { 3 } { 4 } \right)$
C)vertex: (0, 0) focus: $\left( - \frac { 3 } { 4 } , 0 \right)$
D)vertex: (0, 0) focus: $\left( - \frac { 3 } { 16 } , 0 \right)$
E)vertex: $\left( 0 , - \frac { 3 } { 4 } \right)$ focus: $\left( 0 , - \frac { 3 } { 16 } \right)$

Question

Quizplus · Accepted Answer

The given equation is in the form $y^2 = 4px$, where $4p = -\frac{3}{4}$, indicating a parabola that opens to the left. The vertex of this parabola is at the origin (0,0). To find the focus, we solve for $p$: $p = -\frac{3}{16}$. Since the parabola opens to the left, the focus is located at $\left(-\frac{3}{16}, 0\right)$.

Find the Vertex and Focus of the Parabola y2=−34xy ^ { 2 } = - \frac { 3 } { 4 } xy2=−43​x

Find the Vertex and Focus of the Parabola $y ^ { 2 } = - \frac { 3 } { 4 } x$