SAT Math · Desmos

Why Desmos Isn’t Showing the Answer on an SAT Question

What to Check When the Window Is Empty, a Row Shows a Warning, or the Number Matches No Choice

You typed an SAT math question into Desmos, and the answer isn’t on the screen. The window shows no crossing, or an orange triangle sits beside a row, or the number Desmos gives matches none of the four choices. Each of those screens has a cause you can find in a few seconds, and a fix that keeps Desmos doing the work.

When Desmos doesn’t show the answer, check three things in this order: the window, how Desmos read what you typed, and the number you read. The number can go wrong in two ways: it comes from a different point than the one the question asks about, or it’s the right value in a different form from the choices.

Each check takes a click or a glance. Redoing the question by hand takes minutes, on a section that gives you about a minute and a half per question.

What the screen shows points to the fix

Before you change anything, read what the screen shows and what the question asks, because together they point to one fix. Each row below pairs a screen with its fix and links to a question of that kind for you to fix.

  1. Check 1The window

    1. two lines that look paralleland the question asks where they crossZoom outminus button, top right of the graph
  2. Check 2How Desmos read what you typed

    1. an orange triangle beside a rowand the question gives the letter’s valueGive the letter a valuetype it on a row of its own
    2. a sine, cosine, or tangent in a rowand the question marks its angles with a degree signSwitch the angle unitDegrees, under the wrench
  3. Check 3The number you read

    1. several gray points on one curveand the question asks about one moment, such as the landingRead a different pointthe one the question asks about
    2. a decimal that matches no choiceand the question has choices with roots, fractions, or πType the choicesone per row, then compare decimals
On screen
two steep lines, and no top
Question
asks for a rocket’s greatest height

Find a rocket’s greatest height when Desmos shows only two steep lines

This question gives a rocket’s height as an equation and asks for its greatest height. Typed into Desmos exactly as printed, the equation shows two steep lines and no top, which can look like a typing mistake.

Before you retype anything or switch to algebra, run the three checks in order. By hand, the greatest height takes two steps: find the time of the top with t=−b2at = -\frac{b}{2a}, then substitute that time back into the equation, squaring it and multiplying by −4.9-4.9 along the way. Step through the checks below, and answer each step’s question to go on.

A rocket is launched from a platform. Its height hh, in meters, tt seconds after launch is given by h=−4.9t2+39.2t+2h = -4.9t^2 + 39.2t + 2. What is the rocket’s greatest height, in meters?

th
Step 1 of 4

The question gives the rocket’s height hh at every time tt and asks for its greatest height. On a graph of the equation, with tt across and hh up, that height is one point.

Which point on the graph gives the greatest height?

The window is the first thing to check, because zooming out costs a click and changes nothing you typed.

On screen
two lines that look parallel
Question
asks where they cross

Lines look parallel? If their slopes differ, they cross off screen

Two lines that haven’t met yet can look parallel in the window Desmos opens with, while the question asks where they cross. Lines with different slopes always cross somewhere, so when the slopes in the two equations differ, zoom out until the crossing comes into view.

It’s the rocket’s problem again: the answer is outside the window. Trusting the first window leads to “no solution,” which is wrong for any two lines whose slopes differ, and solving by hand means a substitution with decimals in it.

Compare the slopes first, and decide whether these lines cross. Then zoom out with the minus button, and watch for the point where they meet.

What is the solution (x,y)(x, y) to the system of equations y=0.6x+3y = 0.6x + 3 and y=0.5x−2y = 0.5x - 2?

  1. y=0.6x+3y=0.6x+3
  2. y=0.5x−2y=0.5x-2
−55

These lines look parallel. Do they cross?

Keep zooming until the crossing shows, however far out it sits. Lines with equal slopes and different intercepts are the only pair that never crosses, and no zoom changes that, so compare the slopes before you zoom.

On screen
an orange triangle beside a row
Question
gives the letter’s value

An orange triangle means a letter has no value yet

Desmos puts the triangle beside any row that uses a letter it has no value for, such as the kk in g(x)=kx−7g(x) = kx - 7, and offers “add slider” for that letter. The triangle goes away once the letter has a value, and the answer is right only when that value is the one the question gives.

The triangle is the plainest sign of the second check: Desmos read what you typed differently from the way the question means it.

Read what the question gives for kk, then pick the fix that makes both rows use it. Watch what happens to the triangles.

The function gg is defined by g(x)=kx−7g(x) = kx - 7, where kk is a constant. If k=4k = 4, what is the value of g(5)g(5)?

  1. g(x)=kx−7g(x)=kx-7add slider: k
  2. g(5)g(5)add slider: k

What fixes the warning for this question?

A new slider starts its letter at 11, so “add slider” clears the triangles and shows the value of a different function, with no warning left. When a question asks you to find the letter instead, the slider is the right tool: drag it toward the picture the question describes, then check the value exactly before you answer.

On screen
a sine, cosine, or tangent in a row
Question
marks its angles with a degree sign

Before trusting a sine or cosine, set the angle unit the question uses

Desmos reads every angle in either radians or degrees, set under the wrench, and the College Board version on desmos.com starts in radians. Before you trust a sine, cosine, or tangent, set the unit the question uses: degrees when its angles carry a degree sign, and radians when they don’t.

A wrong unit is a misreading Desmos never marks with a triangle. Sometimes it gives a negative length, which is easy to catch, and sometimes a positive number that looks fine.

The first question starts in radians, the unit Desmos starts in. The second starts in degrees, as if you had left the setting there after the first. Set the unit each question uses, and watch the value.

In right triangle ABCABC, angle CC is the right angle, AB=14AB = 14, and angle AA measures 30∘30^\circ. What is the length of BCBC?

ACB30°14?

Question 1 of 2

Set the angle unit this question uses.

  1. 14sin⁡(30)14\sin(30)= −13.8324427373

Desmos keeps the unit you set until you change it, so check the setting on every trig question, even right after you changed it.

On screen
several gray points on one curve
Question
asks about one moment, such as the landing

Start, top, or landing: each gray point answers its own question

Click a curve, and Desmos marks gray points where it crosses each axis and where it turns. Each point answers a different question, so read the one that matches what the question asks.

This is the third check, the number you read. Every gray point is a real number from the right graph, so a wrong one looks just like an answer.

For each question, say in words what its answer describes, the start, the top, or the landing, and then click that point.

A ball is thrown from the roof of a building. Its height hh, in meters, tt seconds after it is thrown is given by h=−5t2+20t+25h = -5t^2 + 20t + 25.

2440th

Question 1 of 2

How many seconds after it is thrown does the ball hit the ground?

Click a gray point on the graph.

A crossing at a negative time still solves the equation, and it describes the ball before anyone threw it. A question about the throw takes its answer from the part of the graph after t=0t = 0.

On screen
a decimal that matches no choice
Question
has choices with roots, fractions, or π

When Desmos’s decimal matches no choice, type each choice in and compare

Desmos gives a solution as a decimal, such as 6.4726.472, and SAT answer choices are often exact, with square roots, fractions, or π\pi. When the decimal matches no choice, type each choice on its own row, and keep the one whose decimal matches.

Like a wrong gray point, this is a problem with the number you read, this time with its form. By hand, matching the decimal means solving exactly, with the quadratic formula and a square root to simplify. Typing the choices takes four short rows and no algebra.

Type each choice into the next row with the keys below, compare its decimal with the point where the line crosses the xx-axis, and then answer.

What is the positive solution to x2−4x−16=0x^2 - 4x - 16 = 0?

−55(6.472, 0)
  1. x2−4x−16=0x^2-4x-16=0

Type a choice into the next row:

Which choice is the positive solution?

A long repeating decimal, such as 0.6666666666670.666666666667, often stands for a fraction, and Desmos can show it as one: click the fraction button at the left end of its row.

Mixed practice

Pick the fix for each screen when nothing labels it

Every screen so far sat under a heading that named its fix. On the test, these screens come mixed in with other questions, and none says what went wrong. Read what each screen shows with what its question asks, and pick the fix before you change anything.

Screen 1 of 5

The question asks where the two lines meet.

  1. y=2x+5y=2x+5
  2. y=2.1x−4y=2.1x-4
−55

Which fix does this screen call for?

Free course · 42 lessons in 8 chapters

Every fix on this page has a lesson in the free Desmos walkthrough

You spot each fix in seconds once you have met its screen a few times on questions you haven’t seen. The walkthrough gives you those questions, and it teaches the steps every fix depends on, such as typing an equation exactly as printed and reading where its graph crosses the xx-axis.

  • You type every line yourself, as you will on test day.
  • Each step is checked before you go on.
  • The practice calculator is built like the one in Bluebook.