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

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Answer 1 · 2015-09-04T15:00:51

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

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 ( $5/3, oo$ )

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