Answer:
[tex]f(x)=(x-1)^2-2[/tex]
Step-by-step explanation:
Equation of a parabola:
[tex]y=a(x-h)^2+k[/tex]
The vertex is given as [tex](h,k)[/tex] -> [tex](1, -2)[/tex]
Plug in both the given point and vertex to find the value of [tex]a[/tex]:
[tex]y=a(x-h)^2+k[/tex]
[tex]y=a(x-1)^2-2[/tex]
[tex]14=a(5-1)^2-2[/tex]
[tex]14=a(4)^2-2[/tex]
[tex]14=16a-2[/tex]
[tex]16=16a[/tex]
[tex]1=a[/tex]
[tex]a=1[/tex]
Therefore, the final function is [tex]f(x)=(x-1)^2-2[/tex]
See attached graph below for a visual of the function.
