Find an equation of a parabola with a vertex at the origin and directrix y = –3.5
y = 1/14 x^2
This is correct!
To verify, we can use the formula for a parabola with vertex at the origin and directrix y = -p, where p is the distance from the vertex to the directrix. In this case, p = 3.5. The formula is:
(y - 0)^2 = 4p(x - 0)
y^2 = 4(3.5)x
y^2 = 14x
Solving for y, we get:
y = ±√(14x)
Since the vertex is at the origin, we only need the positive half of the parabola. The equation y = √(14x) is equivalent to y = (1/14)x^2. Therefore, the equation of the parabola is y = (1/14)x^2.