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 =0.25
Substituting 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]
