Desmos for the SAT · Technique 14 of 23

Build a Table to Test Several x-values at Once

Stop plugging in one number at a time. Evaluate the whole list in one shot.

SolvesWhich value is a solution to the equation?Test the answer choicesEvaluate one function at several x-values

Watch the lesson

The whole move worked on one real SAT question, narrated.

0:00 / 0:00

A second example: four answer choices down one column, and the row that matches the right side read straight off.

A common question hands you an equation and four numbers, then asks which one is a solution. Substituting each choice by hand is slow, and when the choices are decimals, fractions or radicals, it is easy to slip.

Define the side with x in it once, exactly as written, list the four choices in a table, and Desmos fills in the value for all of them in one column. Then scan that column for the row that equals the number on the other side of the equation.

Nothing moves across the equals sign. Rearranging to get a zero is an extra step with a sign in it, and the table does not need it. For $2x^{2} - 3.4x = 1.2$ , define $f(x) = 2x^{2} - 3.4x$ , put the choices down $x_1$ , head the next column $f(x_1)$ , and look for the row that reads 1.2.

Nova

When the four answer choices are numbers, you do not have to solve the equation. Build a table, put all four choices down one column, and Desmos evaluates every one of them at once. Then read off the row that matches the other side.

Now you try it

The rest of the page takes that move slowly. First how it compares with doing the algebra, then the steps in order, then a real SAT question with a live Desmos calculator to try it in.

The algebra way vs the Desmos way

This technique sidesteps solving a decimal quadratic, or substituting each choice by hand.

The question

2x² - 3.4x = 1.2

Which of 0.6, 2, 3 or 5 is a solution?

The algebra way

The quadratic formula on 2x^2 - 3.4x - 1.2 means squaring 3.4 and a square root, by hand.
Or substitute all four choices, each one a decimal squared plus a decimal product.
Either route is a minute of arithmetic where one slip hides the answer.

The Desmos way

Define f(x) = 2x^2 - 3.4x, the left side as written.
Put the four choices in a table column and head the next column f(x_1).
One row reads 1.2, the number on the right side. That is x = 2.

The payoff: All four choices are tested in one keystroke, and the decimals never touch your pencil.

Quick reference

When to reach for a table

The equation looks like...	Do this
x + 5 = 12 (a quick mental solve)	Solve it in your head, do not open a table
2x² - 3.4x = 1.2 (messy quadratic)	Back-solve: test the choices in a table
The choices are fractions or radicals	Back-solve: Desmos evaluates each one for you
x on both sides	Define both sides, f(x) and g(x), and head two columns f(x₁) and g(x₁)

Step by step

The whole move, all 5 steps

Define the side of the equation that has x in it as f(x) = ..., exactly as written. Nothing moves to the other side.
Type table into an empty expression line: Desmos turns it into two columns. Type the answer choices down the x_1 column.
Head the next column f(x_1) to evaluate every choice at once.
Scan that column for the row that equals the number on the other side of the equation. That row is the answer.
If x appears on both sides, define the right side as g(x) too and head a third column g(x_1). The answer is the row where the two columns agree.

The question

The equation $2x^{2} - 3.4x = 1.2$ is given.

Which of the following is a solution to the equation?

A0.6
B2
C3
D5

Step 1 of 4

Define the left side exactly as written: f(x) = 2x² - 3.4x. The 1.2 stays where it is; it is the number you will look for.

In the calculator: f(x)=2x^2-3.4x

No rearranging. Moving the 1.2 across would add a step and a sign to get wrong, and the table does not need it.

Now try it on a real SAT question

Head or scratch paper. One subtraction. Take 61 off both sides and the absolute value is 4, so p is 4. Building a table costs more than the question does.

The equation $|p| + 61 = 65$ is given.

Which value is a solution to the equation?

Pick an answer to get instant coaching from Nova.

Stuck?

Your turnstarts empty

Set this question up yourself, then read the answer straight off the graph.

Worked it out on scratch paper? Type it into Desmos anyway and check. It takes a couple of seconds and it catches the slip you cannot spot by re-reading your own work.

The Desmos trap: when to close the calculator

If you only need to check one x-value, plugging it into the equation by hand is faster than setting up a table.
Table mode is most useful when the answer choices are the candidates. Put all four choices into one column instead of testing them one at a time.
The table header has to be an expression, not an equation. Type $2x_1 - 5$ , never $2x_1 - 5 = 0$ , which throws an error.
The tilde ~ is for regressions, not back-solving, so leave it out here. A plain expression in the header, $f(x_1)$ , is all you need.
The mirror image of this question, four equations tested at one x-value, is Which Equation Represents This Situation?: the same move, with the choices across a list instead of down a column.

If the calculator does something you did not expect

The header has to use the subscript name $x_1$ , as in $f(x_1)$ . Plain $f(x)$ gives the column nothing to evaluate, and it stays blank.

Nova

If you only need to test one value, do that in your head. It's faster than building a whole table. Tables are worth it when you have a list of candidates to check, like all four answer choices, not for a single input.

All Desmos techniques

Put this move into real practice

"Build a Table to Test Several x-values at Once" shows up all over the real SAT. SAT Prep Quest drills the skill at your level, so reaching for it becomes automatic by test day.

Practice free

SAT is a registered trademark of the College Board, which was not involved in producing, and does not endorse, this product. Score estimates are Learner Labs projections, not official College Board scores.