Desmos academy

Memorize this

These are the keystrokes students freeze on in Bluebook. Screenshot the page. Then drill them under a clock — the SAT will not wait for you to remember that ≤ is typed <=.

1. 01

   Vertex form, and how to get h and k

   Standard form $y=a{x}^2+bx+c$. Vertex form $y=a(x-h{)}^2+k$. The vertex is always $(h,k)$. $h=-b/(2a)$. $k$ is $f(h)$, or read it off the graph.

   $y=2(x-3{)}^2+5$ → vertex $(3,5)$

   Don’t expand on the SAT. Graph it and click the gray vertex, or read $h$ and $k$. The sign on $h$ flips: $(x+4)^2$ means $h = -4$.

2. 02

   What a does to a parabola

   $a>0$ opens up (a cup). $a<0$ opens down (a hill). $0<|a|<1$ is wider than $y=x^2$. $|a|>1$ is narrower.

   a = 1, reference

   a = −1, opens down

   a = 0.3, wider

   a = 2, narrower

3. 03

   Circle equation

   $(x-h{)}^2+(y-k{)}^2=r^2$

   Center $(h,k)$. Radius is the square root of the right side — not the right side itself. $(x+2{)}^2$ means $h=-2$. The SAT loves that sign trap. Graph the equation and click the center if you hesitate.

4. 04

   Typing ≤ on the keyboard

   There is no ≤ key in Bluebook Desmos. Type the two characters <= and it becomes ≤. Same for >=. Students who hunt for a special character lose twenty seconds they do not have.

5. 05

   x1, y1 vs x, y

   Graphing a function uses $x$ and $y$: type $y=2x+1$. A table is different. Desmos names the columns $x_1$ and $y_1$ (a second table is $x_2$, $y_2$). Regression has to use those names. $y_1\sim m{x}_1+b$ fits the table. $y\sim mx+b$ tries to define the letter $y$ and ignores the points. If a regression looks empty, you used $x$ instead of $x_1$.

6. 06

   ~ is regression, including higher order

   Tilde is not a statistics class. It is how SAT students fit messy points to a model in ten seconds. Linear is the common case. Module 2 hard has tested quadratic and cubic fits.

   • y1 ~ m x1 + b
   • y1 ~ m x1
   • y1 ~ a x1^2 + b x1 + c
   • y1 ~ a x1^3 + b x1^2 + c x1 + d

   Read the coefficient you were asked for. Don’t copy the whole equation into the SPR box.

7. 07

   cbrt, sqrt, nthroot, mean

   Novice users forget these under time. Type them in lowercase. Roots: sqrt is only square root. cbrt is only cube root. Anything else is nthroot(base, n) or 16^(1/4). Stats: mean([4,11,18]) — the brackets matter. Without a list, Desmos often does nothing useful.

8. Bonus — the one that actually costs points

   Desmos is in radians until you switch it

   SAT trigonometry is in degrees. If you evaluate $\sin (30)$ and get a tiny decimal instead of $1/2$, open the wrench and switch to degrees. Do this once at the start of Math Module 1. Then leave it.