describe the right hand and left hand behavior of the graph of the polynomial function f(x)=2x^2-3x+1

Answer 1

This graph is a second degree polynomial (i.e. the highest power of x is 2). Since 2 is even, the end behaviour will be the same for the left and the right. The leading coefficient (the number in front of the highest power of x - which in this case is 2) is positive. This means both the left and right hand behaviour will be approaching infinity. In proper mathematical speak - you could say that: as x approaches positive infinity, f(x) approaches positive infinity and as x approaches negative infinity, f(x) also approaches positive infinity.