Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin.
Vertical axis and passes through the point (-8,-8)

A) $y ^ { 2 } = - 8 x$
B) $y ^ { 2 } = x$
C) $x ^ { 2 } = - 8 y$
D) $x ^ { 2 } = 8 y$
E) $y ^ { 2 } = 8 x$

Question

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. 
Vertical axis and passes through the point (-8,-8)

A) $y ^ { 2 } = - 8 x$
B) $y ^ { 2 } = x$
C) $x ^ { 2 } = - 8 y$
D) $x ^ { 2 } = 8 y$
E) $y ^ { 2 } = 8 x$

Quizplus · Accepted Answer

Since the parabola has a vertical axis and the vertex at the origin, the standard form of the equation is $x^2 = 4py$, where $p$ is the distance from the vertex to the focus. Given that the parabola passes through the point (-8, -8), we substitute these values into the equation to find $p$. Substituting $(-8, -8)$ into $x^2 = 4py$ gives $64 = -32p$, solving for $p$ gives $p = -2$. Thus, the equation is $x^2 = -8y$.

Find the Standard Form of the Equation of the Parabola y2=−8xy ^ { 2 } = - 8 xy2=−8x

Find the Standard Form of the Equation of the Parabola $y ^ { 2 } = - 8 x$