Drag each tile to the correct box. Arrange the parabolas represented by the equations in increasing order with respect to the y-values of their directrixes.
y = -x2 + 3x + 8
y = 2x2 + 15x + 18
y = x2 + 13x + 5
y = -2x2 + 4x + 8

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1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?