Hello, lance!

Find the equation of the parabola with:

. . [1] Vertex: (0,0)

. . [2] Axis: x-axis

. . [3] Length of latus rectum: 5

From [1], the vertex is at the Origin.

. . The equation is of the form: .

From [2], the parabola is "horizontal": .

. . The equation is of the form: . .(a)

From [3], the length of the latus rectum is 5.

We are expected to know that the length of the latus rectum is

. . Hence: .

Substitute into (a): .

But the parabola can open to the leftthe right.or

. . Therefore: .