# How do you find the equation of a parabola with vertex at the origin and directrix y=-1?

Sep 2, 2017

Equation of parabola is $y = \frac{1}{4} {x}^{2}$

#### Explanation:

Vertex is at $\left(0 , 0\right)$ , Directrix is $y = - 1$

Equation of parabola is  y= a(x-h)^2 + k ; (h,k)  being vertex.

$y = a {\left(x - 0\right)}^{2} + 0 \mathmr{and} y = a {x}^{2}$ . Directrix is below the vertex ,

so parabola opens upward and $a$ is positive . The distance of

directrix from vertex is$D = 1$ , We know $D = \frac{1}{4 | a |}$ or

$1 = \frac{1}{4 | a |} \mathmr{and} a = \frac{1}{4}$ . Equation of parabola is $y = \frac{1}{4} {x}^{2}$

graph{1/4 x^2 [-12.66, 12.65, -6.33, 6.33]} [Ans]