Answer:
The equation of the parabola is [tex](x-3)^2 = 16(y-1)[/tex].
Step-by-step explanation:
It is given that the vertex of a parabola is at the point (3,1), and its focus is at (3,5).
Let the equation of parabola is
[tex](x-h)^2 = 4p(y-k)[/tex]
Where, (h,k) is vertex and (h,k+p) is focus.
The vertex of a parabola is at the point (3,1). So, the equation of parabola is
[tex](x-3)^2 = 4p(y-1)[/tex]
Focus of the parabola is (3,5),
[tex](h,k+p)=(3,5)[/tex]
[tex](3,1+p)=(3,5)[/tex]
Compare both sides.
[tex]1+p=5[/tex]
[tex]p=4[/tex]
Therefore the equation of the parabola is
[tex](x-3)^2 = 4(4)(y-1)[/tex]
[tex](x-3)^2 = 16(y-1)[/tex]
Answer:
a=-2 b=-4 c= 1
Step-by-step explanation:
plug into y=ax^2+bx+c
