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

1 Answer
Gió
Mar 26, 2015

This is a quadratic funtion and the domain is all the Real x. This means that you can give every value of x in the real domain and your function devolves a value of y.

The range is a little bit tricky.
The graph of a quadratic is a PARABOLA...basically a U shaped curve.

The position of the lowes (or highest) point gives us the possibility to "see" the range!
Your quadratic has -3 in front of x^2 so it is a "sad" parábola, a inverted U shaped curve
The highest point is called the Vertex and is given (the coordinates) as (if you have your quadratic in the general form:
ax^2+bx+c=0):
x_v=-b/(2a)
y_v=-Delta/(4a)
with Delta=b^2-4ac

in your case:
x_v=-(-3)/(2*-3)=-1/2
y_v=[9-4(-3*4)]/(4*-3)=4.75

So your range is all the y less or equals to 4.75.

Graphically:
graph{-3x^2-3x+4 [-10.62, 7.16, 1.22, 10.11]}

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