Answer:
[tex]y=-1(x-2)^2+3[/tex]
Step-by-step explanation:
W have been given that the vertex of a parabola is at (2, 3) and the point (0, -1) is also on the parabola. We are asked to find the equation of parabola in the form [tex]y=(x-h)^2+k[/tex].
We know that vertex form of parabola in form [tex]y=a(x-h)^2+k[/tex], where (h,k) in vertex of parabola.
Upon substituting coordinates of vertex, we will get:
[tex]y=a(x-2)^2+3[/tex]
To find the value of a, we will substitute coordinates of point (0, -1) as:
[tex]-1=a(0-2)^2+3[/tex]
[tex]-1=a(4)+3[/tex]
[tex]-1=4a+3[/tex]
[tex]-1-3=4a+3-3[/tex]
[tex]-4=4a[/tex]
[tex]\frac{-4}{4}=\frac{4a}{4}[/tex]
[tex]-1=a[/tex]
Therefore, our required equation would be [tex]y=-1(x-2)^2+3[/tex].
