# What is the equation of the parabola with a vertex at the origin and a directrix of y=1/4?

The equation of parabola is $y = - {x}^{2}$
Equation of the Parabola in Vertex form is $y = a {\left(x - h\right)}^{2} + k$ Here Vertex is at origin so h=0 and k=0 $\therefore y = a \cdot {x}^{2}$The distance between vertex and directrix is $\frac{1}{4}$ so $a = \frac{1}{4 \cdot d} = \frac{1}{4 \cdot \frac{1}{4}} = 1$Here Parabola opens down. So $a = - 1$ Hence the equation of parabola is $y = - {x}^{2}$ graph{-x^2 [-10, 10, -5, 5]}[Answer]