Answer :
Answer:
[tex]\boxed{\bold{y=-5(x-4)^2+1}}[/tex]
Step-by-step explanation:
[tex]y=a(x-h)^2+k[/tex] - vertex form of equation of a parabola where vertex is (h,k)
[tex]y=a(x-4)^2+1[/tex] - vertex form of equation of a parabola where vertex is (4,1)
The parabola goes through point (3, -4) so if x=3 then y=-4
[tex]-4=a(3-4)^2+1\\\\-4-1=a(-1)^2+1-1\\\\-5=a\cdot1\\\\{}\ \ a=-5[/tex]
Therefore the equation of the parabola in vertex form with vertex (4,1), going through point (3,-4):
[tex]y=-5(x-4)^2+1[/tex]