Given that the vertex of the parabola is (4,-3)
The parabola passes through the point (2,-1)
We need to determine the standard form of the equation of the parabola.
Standard form of the equation of the parabola:
The standard form of the equation is [tex]y=a(x-h)^2+k[/tex] where the vertex is (h,k) and a is the constant.
Substituting the vertex (4,-3) in the above equation, we get;
[tex]y=a(x-4)^2-3[/tex] ---------------(1)
Substituting the point (2,-1) in the above equation, we have;
[tex]-1=a(2-4)^2-3[/tex]
[tex]-1=a(-2)^2-3[/tex]
[tex]-1=4a-3[/tex]
[tex]2=4a[/tex]
[tex]\frac{1}{2}=a[/tex]
Thus, the value of a is [tex]\frac{1}{2}[/tex]
Substituting the value of a in the equation (1), we get;
[tex]y=\frac{1}{2}(x-4)^2-3[/tex]
Thus, the standard form of the equation of the parabola is [tex]y=\frac{1}{2}(x-4)^2-3[/tex]
