Question

How do you find the domain and range of `y=3x^2+4x+3`?

Answer 1

The domain is R (all real numbers) or `(-oo,+oo)` and range is (`5/3, oo`)

Explanation:

It is a quadratic function, hence first it can be written vertex form as following:

y= `3(x^2 +4/3 x) +3`

= `3(x^2 + 4/3 x +4/9) -4/3 +3`

=`3 (x+2/3)^2 +5/3`

The function therefore represents a vertical parabola, opening up with vertex at `( -2/3, 5/3)`

The domain is therefore R (all real numbers) or `(-oo,+oo)` and range is (`5/3, oo`)