Question

Find a function whose graph is a parabola with vertex (1, −2) and that passes through the point (5, 14)

Answer 1

`f(x)=(x-1)^2-2`

Explanation:

Equation of a parabola:

`y=a(x-h)^2+k`

The vertex is given as
`(h,k)` ->
`(1, -2)`

Plug in both the given point and vertex to find the value of
`a`:

`y=a(x-h)^2+k`

`y=a(x-1)^2-2`

`14=a(5-1)^2-2`

`14=a(4)^2-2`

`14=16a-2`

`16=16a`

`1=a`

`a=1`

Therefore, the final function is
`f(x)=(x-1)^2-2`

See attached graph below for a visual of the function.