Not infrequently, I have trouble understanding written explanations in the math books and on the web sites I've been using. In this case, the first line of College Board's explanation threw me for a loop:
The function with equation y=(-x)^2+1 and the function with equation y=|x^2+1| each have a minimum value of 1 when x=0...I read this as saying -- as implying -- that x=0 is somehow critical to finding a minimum. Which I (thought I) knew it wasn't.
Mark's explanation cleared things up:
Both of those functions have a minimum value of 1, and that minimum occurs at x=0.
This is why I can't imagine computer-based math courses panning out. Online practice and assessment, yes. Online teaching, no. You need a teacher -- Mark, in this case -- to see why the student doesn't understand and to re-phrase the explanation.
Though I suppose you could write algorithms to try to do what Mark just did. First step: get rid of subordinate clauses --- especially subordinate clauses at the end of sentences, instead of the beginning. From Grammar Bytes:
I am accustomed to putting the most important idea last for emphasis. That's the rule I used reading the CollegeBoard explanation.
Writers use subordination to combine two ideas in a single sentence. Read these two simple sentences:
Rhonda gasped. A six-foot snake slithered across the sidewalk.
Since the two simple sentences are related, you can combine them to express the action more effectively:
Rhonda gasped when a six-foot snake slithered across the sidewalk.
If the two ideas have unequal importance, save the most important one for the end of the sentence so that your reader remembers it best. If we rewrite the example above so that the two ideas are flipped, the wrong point gets emphasized:
When a six-foot snake slithered across the side walk, Rhonda gasped.
A reader is less concerned with Rhonda's reaction than the presence of a giant snake on the sidewalk!