Every SAT math question comes with a built-in Desmos graphing calculator. Here is what to type, what to read, and when to trust the answer, with real screenshots. Free, from the tutors at High Performance Tutoring.
If you practice only five moves before test day, make them these. Tap one to jump to it.
Desmos graphs against x. If the question uses another letter, like \(t\) or \(n\), retype it with x so the graph means what you think.
Wrap fractions in parentheses: (x+1)/(x-3), not x+1/x-3. After ^2 or a fraction, press the right arrow to step back out before you keep typing.
Clicking a graph shows gray dots at its intercepts, turning points, and intersections. Click a dot to see its coordinates.
The home button only resets the default view. Zoom out, or set the axes from the wrench menu to fit the numbers in the problem, so nothing hides off-screen.
Start with these five. Each card shows what to type, what to read, and the mistake to avoid.
\(f(x)\) is defined and the question asks for \(f(7)\), or for a value like \(f(3) - f(1)\).
f(x)=x^2-5x+6f(7)Desmos prints the value at the right of the second line: \(f(7) = 20\).
An equation with one unknown, like \(3(x - 2) = x + 4\).
3(x-2)=x+4Each solution appears as a vertical line. Click where it crosses the x-axis to read it: \((5, 0)\), so \(x = 5\).
A system of equations, "find the solution \((x, y)\)," or "for what x is \(f(x) = g(x)\)?"
y=2x+1y=-x+7Click either line, then click the gray dot where they cross: \((2, 5)\).
"For what values of x does \(f(x) = 0\)?" or "What are the x-intercepts?"
y=x^2-5x+6Click the curve; gray dots appear where it meets the x-axis. Click each one: \((2, 0)\) and \((3, 0)\), so the zeros are \(2\) and \(3\).
The highest or lowest point of a parabola, or a maximum or minimum value.
y=-x^2+4x+1Click the curve, then the gray dot at the turning point: \((2, 5)\).
Two moves for questions built on a list of values.
"Which of these values satisfies...?" or evaluating one function at a list of inputs.
f(x)=x^2-5x+6Then add a table from the + menu, type 1, 2, 3, 4 under x₁, and change the second column's header to f(x1).
The second column fills in on its own: \(2, 0, 0, 2\). So \(x = 2\) and \(x = 3\) make the expression equal 0.
The question gives you a table of numbers and asks for a line of best fit, a slope, or a prediction.
First add a table from the + menu with x₁ = 1, 2, 3, 4, 5 and y₁ = 3, 5, 8, 9, 12. Then, on a new line:
y1~mx1+bDesmos reports the best-fit values under the line: \(m = 2.2\), \(b = 0.8\), so the line is \(y = 2.2x + 0.8\).
Handy, but each needs a final check from you.
"Which point is a solution to the system?" or "Which region shows the solutions?"
y>x+1y<-x+5Each inequality shades its side. The solutions are the region shaded by both, the wedge to the left of \((2, 3)\).
"For what value of \(k\) does \(x^2 - 4x + k = 0\) have exactly one real solution?"
y=x^2-4x+kWhen Desmos offers "add slider" for k, click it.
Graphing \(y = x^2 - 4x + k\) turns the equation's real solutions into x-intercepts. One solution means one intercept, so drag \(k\) until the parabola just touches the x-axis. It looks like \(k = 4\).
Desmos is a tool, not a rule. Solve by hand when it is faster or more exact.
Desmos gives you a correct graph. These five habits keep you from reading the wrong thing off it.
An intersection or zero can sit outside the window. Zoom out before deciding there is none, and confirm no-solution or same-line cases from the equations.
Coordinates Desmos shows can be rounded decimals. If the choices are fractions or radicals, type each choice into Desmos and compare its decimal to the readout. If two choices round to the same value, check by substitution or algebra.
The point is \((2, 5)\), but the question may want 2, 5, or \(2 + 5\). Underline what is being asked.
Desmos can work in radians or degrees. Open the wrench menu and match the setting to the units in the question.
Type \(\tfrac13\) as 1/3, not 0.33. Rounded inputs drift further from the answer with every step.
Official sources: Desmos testing calculator · Bluebook testing tools. Test rules and policies can change; check College Board before test day.
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