diff --git a/.obsidian/plugins/obsidian-git/data.json b/.obsidian/plugins/obsidian-git/data.json index 7b1247f..4bc189e 100644 --- a/.obsidian/plugins/obsidian-git/data.json +++ b/.obsidian/plugins/obsidian-git/data.json @@ -2,7 +2,7 @@ "commitMessage": "vault backup: {{date}}", "autoCommitMessage": "vault backup: {{date}}", "commitDateFormat": "YYYY-MM-DD HH:mm:ss", - "autoSaveInterval": 1, + "autoSaveInterval": 5, "autoPushInterval": 0, "autoPullInterval": 5, "autoPullOnBoot": false, diff --git a/education/math/Quadratics.md b/education/math/Quadratics.md index 7ffa2ac..3a732c4 100644 --- a/education/math/Quadratics.md +++ b/education/math/Quadratics.md @@ -16,6 +16,10 @@ To convert to standard form given a vertex of a quadratic equation and a point t $$ y = a^2 + bx + c $$ # End Behavior of functions If the largest exponent of a function is **even**, both sides of a function will point the same way. -As $x$ goes towards infinity, $f(x)$ will go towards infinity. As $f(x)$ goes towards $-\infty$, $f(x)$ will still go to infinity +Given there's no negative coefficient, as $x$ goes towards infinity, $f(x)$ will go towards infinity. As $f(x)$ goes towards $-\infty$, $f(x)$ will still go to infinity. A negative coefficient will flip this. $$ x \rightarrow \infty, \space f(x) \rightarrow \infty $$ + $$ x \rightarrow -\infty, \space f(x) \rightarrow -\infty $$ +If the largest exponent of a function is **odd**, each side of the function will point towards a different direction. Given there's no negative coefficient, the left side of the graph will point down, and the right side will point up. A negative coefficient will flip this. + +The *least degree* of a polynomial is the number of turning points + 1.