3. Find an equation of a parabola with a vertex at the origin and directrix y = -3.5
Y=-1/14x^2
Y=1/14x^2
Y=1/14y^2
Y=-1/14y^2

Step-by-step explanation:

we know that

The directrix of the parabola is perpendicular to the axis of symmetry of the parabola

In this problem  the directrix is y=-3.5

so

The axis of symmetry is parallel to the y-axis

we have a vertical parabola

Also, the vertex is at the origin

That means-----> the parabola open upward

The equation of a vertical parabola can be written as

where

p is the distance between the vertex and the directrix

In this problem

the distance between the vertex and the directrix is 3.5

----> the value of p is positive because the parabola open upward

substitute

isolate the variable y

25/6

step-by-step explanation:

you multiply 4 by the denominator (4*6=24) and add it to the numerator which makes it 25/6.