What is the domain and range of the quadratic equation y = –2x^2 – 32x – 126?

Question

mathmate · Answer

The domain of a polynomial is all real, i.e. (-inf,inf).
The range depends on the maximum.  So you'll need to find the vertex, and the range will be (-inf,ymax), where ymax is the y-coordinate of the vertex.
To find the vertex, you can use completing the squares, calculus, or the formula
P(-b/(2a), -(b^2-4ac)/4a) where a, b, c are the coefficients of the quadratic function.

anonymous · Answer

ur so smart mathmate

mathmate · Answer

@sunset: thank you for the kind words!

Correction: the range is actually (-inf, ymax], because the value ymax is included in the range.

Also, I forgot to mention that in this particular case where the leading coefficient (the coefficient of x^2) is negative, we look for a maximum.  If the leading coefficient is positive, we look for a minimum, and the corresponding range would be [ymin, +inf).