Question 1203843
given:

Passes through the point ({{{-1}}},{{{5}}})
Vertex is at ({{{0}}},{{{-4}}}) => {{{h=0}}}, {{{k=-4}}}

If a parabola has a horizontal axis, the standard form of the equation of the parabola is this: 

{{{(y - k)^2 = 4p(x - h)}}}

 substitute {{{h=0}}}, {{{k=-4}}}

{{{(y - (-4))^2 = 4p(x - 0)}}}

{{{(y +4)^2 = 4p*x}}}


use given point to calculate {{{4p}}}

{{{(5 +4)^2 = 4p*(-1)}}}

{{{81 = -4p}}}

{{{4p=-81}}}


equation is:

{{{(y +4)^2 = -81x}}}


{{{ drawing( 600, 600, -15, 15, -15, 15,
circle(0,-4,.12),circle(-1,5,.127),
locate(0.2,-4,V(0,-4)), locate(-1,5,p(-1,5)), 
graph( 600, 600, -15, 15, -15, 15, -9sqrt(-x) - 4, 9sqrt(-x) - 4) )}}}