The graph of opens up if and down if Explain why or how that statement is true. (Hint: consider what happens as x gets more and more positive or more and more negative.)
What could be seen or indicated in this type of a scenario is that there is more like an increasing or an increased slope if and when the graph tends to open upwards. On the other hand, if there is a curve that is sort of pointing downwards, that might be indicative of the notion that this might be a graph that has a declining and therefore, more like a reduced slope. So the values of X should tend to increase and therefore go up with a rising slope and an upward graph; on the other hand, the values of X tend to be decreasing and therefore, declining if and when the slope of the graph tends to go downward.
f(x)=-x^2. This opens up downward. As x^2 gets larger, -x^2 gets larger negative, so the graph goes down with increasing positive or negative x. f(x)=x^2, here, when x is positive or negative x^2 is always positive, like the first case. But there is no negative sign in front of the x^2, so the graph opens upward.