Find the vertex and focus of the parabola. $y ^ { 2 } = - \frac { 9 } { 2 } x$
A)vertex: (0,0) focus: $\left( - \frac { 9 } { 8 } , 0 \right)$
B)vertex: $\left( 0 , - \frac { 5 } { 4 } \right)$ focus: $\left( - \frac { 9 } { 2 } , - \frac { 9 } { 2 } \right)$
C)vertex: (0,0) focus: $\left( 0 , - \frac { 9 } { 2 } \right)$
D)vertex: $\left( 0 , - \frac { 5 } { 4 } \right)$ focus: $\left( 0 , - \frac { 9 } { 8 } \right)$
E)vertex: (0,0) focus: $\left( - \frac { 9 } { 2 } , 0 \right)$

Question

Quizplus · Accepted Answer

The given equation is in the form $y^2 = 4px$, where $4p = -\frac{9}{2}$, so $p = -\frac{9}{8}$. The vertex of a parabola in this form is at the origin (0,0), and the focus is $p$ units away from the vertex in the direction of the parabola's opening, which is to the left in this case, making the focus $\left(-\frac{9}{8}, 0\right)$.

Find the Vertex and Focus of the Parabola y2=−92xy ^ { 2 } = - \frac { 9 } { 2 } xy2=−29​x

Find the Vertex and Focus of the Parabola $y ^ { 2 } = - \frac { 9 } { 2 } x$