Which of the quadratic functions has the widest graph? A. y = (1/3)x^2 B. y = -4*x^2 C. y = 0.3*x^2 D. y = (-4/5)x^2

The graph of the function of the form y = a*x^2 becomes more
steep as the value of a in increases. For the same increase in x the value of y changes by a
larger extent as x is being multiplied by a larger coefficient. For a smaller value of a , the
graph is wider in nature.

To find the function which has the widest
graph we need to compare the absolute value of a, if a is negative it means the quadratic graph
opens downwards but how wide the graph is depends on the magnitude of
a.

For option A, |a| = (1/3), for option B it is |-4| = 4, for
option C it is |0.3| = 0.3 and for option D it is |-4/5| = 0.8

The
smallest magnitude of a is in option C.

Therefore the
widest graph is of the function defined in option C.