Write an equation for the parabola with vertex at the origin.
-Through $( \sqrt { 2 } , 2 )$, opening upward
A) $x = y ^ { 2 }$
B) $x = \frac { \sqrt { 2 } } { 2 } y ^ { 2 }$
C) $y = x ^ { 2 }$
D) $y = 2 x ^ { 2 }$

Question

Quizplus · Accepted Answer

Since the parabola opens upward and has its vertex at the origin, the standard form is $y = ax^2$. Substituting the point $(\sqrt{2}, 2)$ into this equation gives $2 = a(\sqrt{2})^2$, which simplifies to $2 = 2a$, leading to $a = 1$. Therefore, the equation is $y = x^2$.

Write an Equation for the Parabola with Vertex at the Origin