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

1 Answer
bp
Sep 4, 2015

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#)

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