Answer:
[tex]y=-(x+1)^2+4[/tex]
Step-by-step explanation:
we know that
[tex]y=a(x-h)^2+k[/tex]
Is the equation of a vertical parabola written in vertex form
where
(h,k) is the vertex
a is the leading coefficient
In this problem we have
The vertex is the point (-1,4)
so
[tex](h,k)=(-1,4)[/tex]
substitute
[tex]y=a(x+1)^2+4[/tex]
Find the value of a
we have the ordered pair (0,3)
substitute the value of x and the value of y in the quadratic equation and solve for a
[tex]3=a(0+1)^2+4[/tex]
[tex]3=a+4\\a=3-4\\a=-1[/tex]
therefore
[tex]y=-(x+1)^2+4[/tex]
