What is an equation of a parabola with the given vertex and focus? vertex 0,0 focus 2.5 0?

The equation of a parabola with the vertex and focus vertex (0 0) focus (2.5, 0) is,[tex](y-0)^2=10(x-0)[/tex]What is the vertex form of parabola?Vertex form of parabola is the equation form of quadratic equation which is used to find the coordinate of vertex points at which the parabola crosses its symmetry.The standard equation of the vertex form of parabola is given as,[tex]4a(y-k)=(x-h)^2[/tex]Here, (h, k) is the vertex point.A parabola has vertex and focus vertex  as (0 0) focus (2.5,0). The value of a is,[tex]a=2.5-0\\a=2.5[/tex]Which is positive. Thus, the equation which is used for this case is,[tex](y-k)^2=4a(x-h)[/tex]Put the values as,[tex](y-0)^2=4(2.5)(x-0)\\(y-0)^2=10(x-0)[/tex]Thus, the equation of a parabola with the vertex and focus vertex (0 0) focus (2.5, 0) is,[tex](y-0)^2=10(x-0)[/tex]Learn more about the vertex form of the parabola here;