2. A train first travels east for 20 kilometers. Then it turns north and travels for 43 kilometers. Next it goes west for 20 kil
ometers. Finally, it travels south for an unknown number of kilometers. At the end of the journey, the train is back at the original location. How far did it travel southward?
a) True. Plug in x = 0 and it leads to y = c. Therefore, the point (0,c) is on the parabola.
b) False. Plug in y = 0 and apply the quadratic formula. One x intercept may sometimes be x = c, but it could easily be other values as well. Or perhaps you may not get any real number solutions at all. See part d) below.
c) True. If a < 0, then the leading coefficient is negative. Overall, both endpoints will tend toward negative infinity to produce a parabola that opens downward.
d) False. The quadratic may have one x intercept or it may not have any x intercepts at all. It depends on what the discriminant d = b^2 - 4ac is equal to. If d < 0, then we have no x intercepts. If d = 0, then we have exactly 1 x intercept. If d > 0, then we have two different x intercepts.
e) True. The vertex's x coordinate is -b/(2a). If b = 0, then the x coordinate of the vertex is 0. The vertical line x = 0 is directly on top of the y axis.
