Question

How do you find the range of `f(x)=5x^2+2x-1`?

Answer 1

Range: `{f(x) in RR: f(x) >= -6/5}`

Explanation:

`f(x) = 5x^2 + 2x - 1`

Method 1: Completing the squares
`f(x)= 5(x^2 + 2/5x + 1/25 - 1/25) - 1`
`= 5(x + 1/5)^2 - 6/5`

Method 2: Stationary points
`f'(x)= 0`
`10x = -2`
`x = -1/5, f(-1/5) = -6/5`

Minimum point `(-1/5,-6/5)`

Hence range: `{f(x) in RR: f(x) >= -6/5}`

graph{5x^2+2x-1 [-2, 2, -5, 5]}