equation of parabola in vertex form that had vertex at -3,-19 and pass through 5,-3

Answer:The standard parabolic equation is [tex]y = 0.25(x  +3)^2 -19[/tex]Step-by-step explanation:Here, the vertex of parabola is (h,k)  = ( -3,-19)The points on the given parabola is ( 5,-3)Now, the general form of the Parabolic Equation is [tex]y = a(x - h)^2 + k[/tex](1) Substitute Coordinates (h,k) for the Vertex[tex]y = a(x - h)^2 + k \implies y = a ( x - (-3)) ^2 + (-19)\\or, y = a( x+3)^2 - 19[/tex](2)Substitute point Coordinates (x,y)[tex]y = a( x+3)^2 - 19  \implies-3 = a(5+3)^2 -19\\or, -3 = 64 a -19\\\implies 64 a = 16\\or, a = 16/64 = 0.25[/tex]⇒ a  =0.25Substituting the values of (h,k) and a in the standard for, we get,The standard parabolic equation is [tex]y = 0.25(x  +3)^2 -19[/tex]