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...

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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.**

The widest graph is when the coefficient of x has the smallest value.

For equation A, the absolute value of the coefficient is (1/3)=0.3333...

For equation B, the absolute values of the coefficient is (4)

For equation C, the absolute values of the coefficient is (0.3)

For equation D, the absolute values of the coefficient is (4/5)=0.8

Then we notice that equation C has the widest graph.

**Then the answer is C) y= (0.3)x^2**