Question

write the equation for the quadratic function that has the vertex at (1,3) and passes through the point (0,5)

Answer 1

For this quadratic, its vertex form
`f(x) = a(x-h)^2+k` is
`f(x) = a(x-1)^2+3`.

To find the value of a, plug in (0,5) and solve.


`5 = a(0-1)^2+3 \\ a = 2`

The final equation in vertex form is
`f(x) = 2(x-1)^2+3`.

In standard form
`f(x) = ax^2+bx+c`, the function is
`f(x) = 2x^2-4x+5`.