Find p in Parabola Problem with {x | -50 < x < 50}, {y | 0 < y < 20}

[yourmom98]

Given {x | -50 < x < 50}, {y | 0 < y < 20} vertex at (0,20) it is a parabola find the equation in (x-h)^2=4p(y-k)

its pretty easy except how do i find p?

 

[HallsofIvy]

The information you given isn't enough- I assume you mean a parabola with vertical line of symmetry, vertex at (0, 20), and such that when x=50, y= 0.
(From {x|-50< x< 50}, {y|0< y< 20}, my first guess was x= 50, y= 20 but then I saw that the vertex was at y= 20 so the parabola must be opening downward.)

Since you only ask about p, I assume you understand that since the vertex is at (0, 20), the equation is (x- 0)²= 4p(y- 20). Now, put x= 50, y= 0 in that and solve for p.

 

[quicknote]

To find the value of p in this parabola problem, we can use the fact that the vertex of the parabola is given at (0,20). This means that the parabola is symmetric about the y-axis, and the equation will take the form (x-h)^2 = 4p(y-k), where (h,k) is the vertex. In this case, h = 0 and k = 20, so the equation becomes x^2 = 4p(y-20).

To find the value of p, we can use the fact that the parabola passes through the point (50,0). Substituting these values into the equation, we get:

50^2 = 4p(0-20)
2500 = -80p
p = -2500/80
p = -31.25

Therefore, the equation of the parabola is (x-0)^2 = -125(y-20), or simplified, x^2 = -125y + 2500. This equation represents a parabola with a vertex at (0,20) and a focus at (0, -31.25).