It is given that the parabola has the vertex at (2,-1)and y intercept of 3,
Consider the general equation of the parabola with vertex (p,q),
[tex]y=a(x-p)^2+q[/tex]Sbstitute 2 for 'p' and -1 for 'q',
[tex]y=a(x-2)^2-1[/tex]Given that the y-intercept is 3, it means that the curve passess through (0,3),
So it must satisfy the equation,
[tex]3=a(0-2)^2-1\Rightarrow4a=4\Rightarrow a=1[/tex]Substitute the value of 'a', 'p', and 'q' in the standard equation,
[tex]y=1(x-2)^2-1\Rightarrow y=(x-2)^2-1[/tex]Thus, the equation of the parabola can be obtained using the given conditions.
