Question

What is the range of the function `y=4x^2+2`?

Answer 1

See explanation.

Explanation:

Graph of this function is a parabola with vertex at `(0,2)`. The function's values go to `+oo` if `x` goes to either `-oo` or `+oo`, so the range is:

`r=(2,+oo)`

The graph is:

graph{4x^2+2 [-10, 10, -5, 5]}

Answer 2

Range: `[+2,+oo)`

Explanation:

`y = 4x^2+2`

`y` is a quadratic function of the form `ax^2+bx+c`
Where: `a=+4,b=0 and c=+2`

`y` will have a parabolic graph with axis of symmetry where `x=-b/(2a)`

`:. x=0`

Since `a>0` `y` will have a minimum value at `x=0`

`:. y_min = +2`

Since, `y` has no finite upper bound the range of `y` is `[+2,+oo)`