To find the x-intercept on Desmos, graph the equation and click where it crosses the x-axis; the point shows (x, 0). For y = 2x - 6, the gray point reads (3, 0), so the x-intercept is 3. A graph can have one x-intercept, several, or none, and this guide covers all three cases.
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Question banks: October 2026 Math question bank
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You can follow along on the College Board version of Desmos on our Desmos on the SAT page. Bluebook has Desmos built in, and College Board allows a calculator on the entire Math section. If the question also asks for the y-intercept, read how to find x- and y-intercepts on Desmos first. This page goes deeper on the x-axis: zeros, graphs with several crossings, and what to do when Desmos is not showing an x-intercept.
The rule: an x-intercept is a zero
You just learned how to find an x-intercept on Desmos. Now see if it sticks on an SAT Math section — take one for free, no card needed.
Start 1-day free trial →An x-intercept is a point where y = 0. SAT questions name the same x-value four ways, so learn to spot all of them:
- the x-intercept of the graph of y = f(x)
- a zero of the function f
- a root, or a solution, of the equation f(x) = 0
- a value of x where the graph meets the x-axis
Count before you calculate. A line that is not horizontal has exactly one x-intercept. A parabola has 0, 1 or 2. A cubic has 1, 2 or 3. When a question asks "how many", you are counting points on the x-axis, not solving for one number.
Three ways to find the x-intercept on Desmos
1. Click the graph. Desmos calls the marked spots points of interest. Its help center says they show in gray once you select the curve, either on the graph or on its expression line. Hover over a gray point to read its coordinates, or select it to keep the label on screen. Gray points also mark the y-intercept, maximums, minimums and intersections, so keep only the ones with 0 as the y-coordinate (Desmos Help Center, Getting Started and FAQs).
2. Use a function table. Write the function in function notation, such as f(x) = 2x - 6. Click Edit List on that line and choose the table option. The table starts with x from -2 to 2. Type any other x-values into the left column, and look for a row where the output is 0. This works well for checking an answer choice: type the choice as an x-value and see if f(x) comes out as 0.
3. Graph the x-axis as a second line. Type y = 0 on a new line. Desmos marks the points where two graphs intersect, so the crossings between your curve and y = 0 are the x-intercepts. The same move solves any equation of the form f(x) = g(x); for two full equations, see how to solve systems of equations on Desmos.
Worked example: a cubic with three x-intercepts
SAT-style question: The function f is defined by f(x) = x3 - 2x2 - 5x + 6. The graph of y = f(x) in the xy-plane has how many x-intercepts, and what is the sum of their x-coordinates?
1 f(x) = x^3 - 2x^2 - 5x + 6- Type the function on line 1 in function notation. That keeps the table method one click away if you need it.
- Click the curve. Gray points appear.
- Sort them. Three sit on the x-axis: (-2, 0), (1, 0) and (3, 0). One sits on the y-axis at (0, 6). Two are turning points, near x = -0.79 and x = 2.12. Only the first three are x-intercepts.
- Answer the question that was asked. There are 3 x-intercepts, and -2 + 1 + 3 = 2.
Check by hand: f(1) = 1 - 2 - 5 + 6 = 0, so (x - 1) is a factor. Dividing leaves x2 - x - 6 = (x - 3)(x + 2). The zeros are 1, 3 and -2, and their sum is 2. Both methods agree.
See which question types are costing you points
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Guided example: an x-intercept that is a fraction
SAT-style question: The function g is defined by g(x) = 2x2 - 3x - 5. What is the positive x-intercept of the graph of y = g(x), written as a fraction?
1 g(x) = 2x^2 - 3x - 5- Graph g and click the parabola. The two gray points on the x-axis read (-1, 0) and (2.5, 0).
- The question wants the positive one, so ignore -1.
- Your step: turn 2.5 into a fraction and confirm it with the table method.
Check your answer: 2.5 = 5/2. In a table for g, type 2.5 in the x column and the output is 0, because 2(6.25) - 7.5 - 5 = 0. By hand, 2x2 - 3x - 5 = (2x - 5)(x + 1), which gives x = 5/2 or x = -1.
Practice this now: the free Quadratic Functions lesson notes cover quadratic functions. For lines, use the free Lines and Linear Relationships lesson notes.
Desmos not showing the x-intercept? Five checks
- Select the curve. Gray points show only after you select the graph or its expression line, so click on the curve itself.
- Ask whether the graph reaches the x-axis. The parabola y = -x2 + 4x - 7 opens down and peaks at (2, -3), so it stays below the axis and has no x-intercepts. The discriminant agrees: 42 - 4(-1)(-7) = -12, and a negative discriminant means no real zeros. On the SAT, "no x-intercepts" and "no real solutions" are the same answer.
- Look outside the window. A tank holds V = 1,350 - 18t gallons of water t minutes after it starts draining. The x-intercept is (75, 0), which can sit far to the right of the starting view. Drag the graph, click Zoom Out, or open Graph Settings and set the x-axis from 0 to 100 (Desmos Help Center, Navigate a Graph). In context, 75 is the number of minutes until the tank is empty.
- Watch for a graph that touches and turns. f(x) = x3 - 3x + 2 factors as (x - 1)2(x + 2). It crosses at x = -2 but only touches the axis at x = 1, where it also has a turning point. That gives 2 x-intercepts, not 3. Zoom in near x = 1 and trust the factored form for the count.
- Still nothing? Add
y = 0on a new line and click where the graphs meet, or type the point you expect, such as(75, 0), and see whether it lands on the graph.
Your turn
Problem 1. The function p is defined by p(x) = -2x2 + 8x + 10. What is the positive x-intercept of the graph of y = p(x)?
Problem 2. The function h is defined by h(x) = x2 + 6x + k, where k is a constant. For what value of k does the graph of y = h(x) have exactly one x-intercept?
Problem 3. A company's profit, in dollars, from selling n items is P(n) = 40n - 1,800. What is the x-intercept of the graph of y = P(n), and what does it mean?
Answer 1: 5. The gray points on the x-axis are (-1, 0) and (5, 0). By hand, -2(x2 - 4x - 5) = -2(x - 5)(x + 1).
Answer 2: k = 9. One x-intercept means the discriminant is 0: 62 - 4(1)(k) = 0, so k = 9. Graph y = x2 + 6x + 9 to check: it touches the x-axis only at (-3, 0).
Answer 3: (45, 0). 40n = 1,800 gives n = 45. At 45 items sold, the profit is 0 dollars, so 45 is the break-even point.
When algebra is faster
College Board's calculator policy says some Math questions are better done without a calculator. If the function is already factored, as in y = (x - 7)(x + 3), you can read the x-intercepts 7 and -3 straight away. For a line such as y = 4x - 10, set y = 0 and divide: x = 5/2. Graph when the polynomial does not factor at a glance, when you need to count crossings, or when you want to check a zero you found by hand.
Mistakes to avoid
- Reading the wrong gray point. In the worked example, (0, 6) and the two turning points are gray too. An x-intercept has 0 as its second coordinate.
- Copying a rounded decimal. The x-intercept of y = 3x - 2 is 2/3. If the label shows 0.667, match it to 2/3 before you pick an answer choice.
- Counting a touch as two points. A graph that touches the axis and turns back gives one x-intercept at that spot, as in (x - 1)2(x + 2).
Practice next
Work through both lesson notes above until zeros feel routine, then mix them with other topics in the TTA SAT question bank. For the other half of the axis, read how to find the y-intercept on Desmos. The Desmos on the SAT guide collects the rest of the calculator techniques.
Checked against College Board's calculator policy and the Desmos Help Center article "Getting Started: Desmos Graphing Calculator" on September 26, 2026. Every intercept on this page was recomputed before publishing. The Test Advantage is independent of College Board and Desmos.
Frequently Asked Questions
What is an x-intercept?
A point where the graph meets the x-axis, so y = 0 there. Its x-value is also called a zero of the function, a root, or a solution of f(x) = 0.
Why is Desmos not showing the x-intercept?
Select the curve first: Desmos shows its gray points of interest after you click the graph or its expression line. If none appear on the x-axis, zoom out or set the window in Graph Settings. Some graphs never reach the x-axis; y = -x^2 + 4x - 7 peaks at y = -3.
Can I find x-intercepts with a table on Desmos?
Yes. Write the function as g(x) = ..., click Edit List and make a table, then type x-values in the left column. A row where the output is 0 is an x-intercept. For g(x) = 2x^2 - 3x - 5, x = -1 and x = 2.5 both give 0.
How many x-intercepts can a graph have?
A line that is not horizontal has one. A parabola has 0, 1 or 2. A cubic has 1, 2 or 3: x^3 - 2x^2 - 5x + 6 crosses at -2, 1 and 3, while x^3 - 3x + 2 has only two because it touches the axis at x = 1.
What does an x-intercept mean in a word problem?
It is the input that makes the output 0. If a tank holds V = 1,350 - 18t gallons after t minutes, the x-intercept (75, 0) means the tank is empty after 75 minutes.