Answer: 

The graphs are both parabolas, have the same vertex of (0, 0) and are both concave up. 

The rates of change are not equivalent.  The rate of change of  y = 2x² is twice the rate of change of x². 

When x = 3, the value of y in the equation y = 2x² is equal to 18.  

When x = 3, the value of y in the equation y = x²  is equal to 9.  18 is twice the value of 9.

DEFINITIONS:

Parameter -- a single number that describes some aspect of an entire population.  Whereas, a statistic is an estimate of that value computed from some sample of the population.[1]

Quadratic function -- a function whose value is given by a quadratic polynomial.  The graph of the function is the graph of y = ax² + bx + c; it is a parabola with a vertical axis; the vertex is the low point or high point according to whether a is positive or negative.  The solutions of the quadratic equation ax² + bx + c = 0 are called the zeros of the quadratic function; they specify the points of the graph where y = 0 (the intersection with the x-axis).  The graph crosses the x-axis twice, once, or not at all according to whether the discriminant b² – 4ac of the quadratic equation is positive, zero, or negative. [2]

Exponential function -- a function of the form f (x) = ab^x, where  a ≠ 0, b > 0, b ≠ 1, and x is a real number. Note: e^x is called the natural exponential function where e is the irrational number 2.718281828 correct to ten significant figures.  It is often shown on a calculator as “exp” and the exponential function is often written as exp(x).[3]

Teacher NoteS:

Students should also discuss the shape of each graph. The shape of the first graph will be more narrow because the rate of change is twice the rate of change in the second graph.