Given: The parabola shown
To Determine: The equation of the parabola
Solution
The equation of a parabola given the vertex and a point is given as
[tex]\begin{gathered} y=a(x-h)^2+k \\ Vertex=(h,k) \\ a=stretch-constant \end{gathered}[/tex]
From the graph, we locate the vertex and the a point A as shown below
So
[tex]\begin{gathered} Vertex=(3,-2) \\ PointA:(4,-1) \end{gathered}[/tex]
Substitute the vertex and the point A to get the value of a
[tex]\begin{gathered} y=a(x-h)^2+k \\ -1=a(4-3)^2+(-2) \\ -1=a(1)^2-2 \\ -1=a-2 \\ -1+2=a \\ 1=a \end{gathered}[/tex]
Substitute the value of a and the vertex to get the equation of the parabola
[tex]\begin{gathered} y=a(x-h)^2+k \\ y=1(x-3)^2+(-2) \\ y=(x-3)^2-2 \end{gathered}[/tex]
Hence, the equation of the parabola is
y = (x -3)² - 2
