Transcript:
[after finding constants a, b, c correctly for a parabola y = ax^2 + bx + c both in terms of a roadway context and numerically using derivative formulas, we ask Wade to identify the full equation for this parabola.]
WADE: Is that all that [the previous part] is asking for? Just to find c, b, and a?
INTERVIEWER: (nods)
WADE: Gotcha. Okay, next problem. “Which of the following is the correct equation of the parabola? Checkmark your choice.” So we know that it starts at, I’m assuming we’re using this guy down here [indicates roadway graph at bottom of page] for this equation, so we know that it starts here at 1.25. That’s basically our y-intercept. So we can get rid of this guy [crosses out first possible answer].
INTERVIEWER: Sorry, why? Just for the record.
WADE: Oh, sorry, because this constant back here, c, [points to multiple choice equation] that’s the y-intercept. So obviously, that just doesn’t match this 0.01. So, instinctually I would know that the rate of change of the slope would typically be greater than the slope itself. Is that correct?
Oh, wait, I can calculate it! So I can just do rise over run through the whole parabola if I’m not mistaken.
So I would do 2.75 – 1.25, divided by this length of 10. Oh, but because it’s the parabola, we have a point of vertical intersection at the middle, so that means the slope would have to be higher than the one that I calculated, because it would undercut the curve here. So that tells me that the slope would be likely 0.25. So that leaves this one out as well.
And typically in highway problems, the rate of change of the slope is very low. Obviously, that’s something I’ve learned from doing highway engineering courses. But because of that, I’m inclined to think this one is the only reasonable answer.
Yvonne Lai 