Hi, Mike! Can you explain the second way we can approach question number 6 from the Parabola chapter? (The two points where the higher y-coordinate is also farther from the line of symmetry.) It would be great if you can provide an example. Thank you.

Sure. Here’s the question:

The key, as I say in the solution, is to look for points that are consistent with what you know about the parabola given the equation: that it opens upwards and that its line of symmetry is at *x* = 6. Because parabolas get wider and wider, points in a parabola that opens up must get higher and higher the farther they get from the line of symmetry.

Therefore, you’re looking for either

- Two points with the same
*y*-coordinate that are the same distance from the line of symmetry, or - Two points that are otherwise consistent with the shape of an upwards-opening parabola that’s symmetrical about
*x*= 6.

Choice D does the first one—*x* = 2 and *x* = 10 are each 4 away from the line of symmetry at *x* = 6, and both points have the same *y*-coordinate of –5.

No choice satisfies the second one (otherwise there’d be more than one possible right answer!) but a choice like (4, 10) and (9, 15) would. (4, 10) is closer to *x* = 6 and has a lower *y*-value; (9, 15) is farther from *x* = 6 and has a higher *y*-value: