An x-intercept is where a graph meets the horizontal axis, so its output is . If a function is given as a formula, graph it in Desmos and click the points on that axis. Read the -coordinate, not the height. If there are two intercepts, a condition like positive tells you which one to keep.
Hints
- Hint 1
An x-intercept has output because it lies on the horizontal axis. That turns the graph question into . The question wants the input that produces that output, not the output itself.
- Hint 2
A square root gives a nonnegative output, so this graph won't dip below the horizontal axis. Enter the function in Desmos, click where the curve meets that axis, and check which horizontal coordinate has the requested sign.
Step-by-step
Graph and read the intercept
Step 1Turn the intercept into an output
At an x-intercept, the output, or height, is . So the positive x-intercept asks for a positive input that satisfies:
- Step 2
Click the positive intercept
Type in Desmos. Click the curve, then click its two endpoints on the -axis. Desmos shows and . The x-coordinate is the first number in each point, so the positive one is . Use output to locate an x-intercept, then report the coordinate the question asks for. Grid in 3.
Lessons that teach this
- SAT Nonlinear FunctionsIntermediateCoreRead nonlinear graphs and representations
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- SAT Advanced AlgebraIntermediateSolve quadratic equations by factoring
- DesmosBeginnerCoreRead points of interest from a graph
- DesmosBeginnerSolve one-variable equations