For the question (#9) that says “For which of the following lines or curves…could have neither an x-intercept nor a y-intercept”
Technically, it is possible to graph a parabola that never touches the x-intercept or the y-intercept Greg however rules it out by saying a parabola has to have either an X or a Y intercept. What am I missing here?
A quadratic equation is of the form y = ax^2 + bx + c, and the y intercept corresponds to the value when x = 0.
If you sub in x = 0, then you’re left with y = c, so i don’t see why you should never have at least a y intercept.
Alternatively, if you consider the end behavior of a parabola, you either have the y value approaching \pm \infty as x \to \pm \infty; therefore, it must cross the y axis at some point.