Question

ompare the graphs of the following group of​ functions, and list them in order from widest to narrowest.
y equals negative 9 x squaredy=−9x2​, y equals negative 8 x squaredy=−8x2​, y equals negative 4 x squaredy=−4x2

Answer 1

All three are downward-opening parabolas with vertex at (0,0). The width is determined by |a| in y = a x^2: larger |a| → narrower.

From widest to narrowest:
1. y = −4x^2 (widest, |a| = 4)
2. y = −8x^2 (middle, |a| = 8)
3. y = −9x^2 (narrowest, |a| = 9)

(For example, at x = 1 the y-values are −4, −8, −9, so −9x^2 drops fastest and is steepest/narrowest.)