Question

Form quadratic functions given the following information: f(x)>0 if and only if 1

Answer 1

`f(x) = - 2( {x - 3)}^(2) + 8`

Explanation:

The quadratic function in the vertex form is:

`f(x) = a( {x - h)}^(2) + k`

From the given information, k=8 and h is the midpoint of 1 and 5 which is 3

`f(x) = a( {x - 3)}^(2) + 8`

f(1)=0

`0 = a( {1 - 3)}^(2) + 8`

`- 8 = 4a`

`a = - 2`

The required equation is

`f(x) = - 2( {x - 3)}^(2) + 8`