Typing Math in Desmos

An SAT question gives you $y = \tfrac{1}{2}x + 3$. You type it as written, y=1/2x+3, and Desmos builds $y = \frac{1}{2x + 3}$: a curve instead of a line, and every value you read off it is wrong.

The slash opens a stacked fraction, and the denominator holds on to everything you type next. A space does not get you out, it goes into the denominator too. Neither do parentheses: type y=(1/2)x+3 and the closing parenthesis lands inside the fraction as well, giving you $y = \frac{1}{(2)x + 3}$. That is the natural fix to reach for, and it does not work.

What does work is the right arrow. Finish the bottom of the fraction, press the right arrow key once to step back out to the baseline, then keep typing. For a half in particular you can also dodge the fraction entirely and type .5x+3, which Desmos leaves alone.

You never hunt for symbols in Desmos: type the word sqrt and it becomes a root sign with a box to fill, and pi becomes the symbol. Other functions are typed as words too: gcd(12,18) reads 6 and lcm(4,6) reads 12.

A root then behaves like a fraction, not like an exponent. Type sqrt9+1 and the +1 goes under the root sign, so you get $\sqrt{9 + 1} \approx 3.16$ when you wanted $\sqrt{9} + 1 = 4$. Fill the box, press the right arrow, then carry on.

cbrt behaves exactly the same. cbrt27 builds $\sqrt[3]{27} = 3$, and cbrt27+1 puts the +1 under the sign and hands you about 3.04. The right arrow first, then +1, gives you 4.

nthroot is the one exception: its cursor starts in the small index box, so type the index, press the right arrow, then type what goes under the root (nthroot, 3, right arrow, 27 builds $\sqrt[3]{27}$).

Press ^ (or the squared button on the keypad) and type the power. The moment you type an operator like +, - or =, Desmos drops you back down to the baseline on its own. So x^2+3x comes out as $x^{2} + 3x$ with no extra keys, and so does the whole of a quadratic.

The one exception is when the next thing you type after the exponent is a letter or a digit. Type x^2 and then y and the y climbs into the power too, giving $x^{2y}$, which is a different curve entirely. That is the moment for the right arrow.

Growth and decay models stack both traps at once. Something like $y = 500 \cdot 2^{x/3} + 100$ puts you inside a fraction, inside an exponent: two levels off the baseline, so two right arrows to get back. Typed straight through you get $y = 500 \cdot 2^{\frac{x}{3 + 100}}$, which is nearly a flat line.

Press the arrow once and you step out of the fraction only. Press it again and you are back on the baseline, where the + 100 belongs. When you are not sure where you are, look at the cursor: its height tells you which level you are standing on.

Lists and tables use names like $L_{1}$, $x_{1}$ and $y_{1}$. You never type the underscore: type L then 1 and Desmos drops the 1 into a subscript for you. Same for x1 and y1, which is why a regression model is typed as y1 ~ mx1 + b and comes out as y-one tilde m x-one plus b.

Where you meet this: the list and table controls from the interface lesson, and the regression technique in particular.

For absolute value bars, type the | key (Shift and the backslash key, above Enter on most keyboards), type what goes inside, then type | again, and you get $y = |x - 3|$. The on-screen keypad has a bars button too.

Typing abs(x) also works and graphs the same thing, but it stays on screen as the word abs rather than turning into bars, so the key is the cleaner habit when you are matching an answer choice.