rom the point it passed We were given
Vertex = (3,1)
Point = (2, -2)
The equation of the parabola is given by:
[tex]y=a(x-h)^2+k[/tex]where (h, k) is the vertex = (3,1)
a is a cnstant
On substitution:
[tex]y=a(x-3)^2+1[/tex]Substituting the value of (x,y) from the point it passed through to find a:
[tex]\begin{gathered} y=a(x-3)^{2}+1 \\ \\ -2=a(2-3)^2+1 \\ \\ -2=a+1 \\ \\ a=-3 \end{gathered}[/tex]Therefore substitute a into the original equation:
[tex]y=-3(x-3)^2+1[/tex]The equation of the parabola is given by:
y = -3(x-3)^2 + 1
