Finding Intersections in Desmos
Solve Systems Fast
Build equations from context, spot patterns fast, and practice with intent.
Why the SAT Emphasizes Finding Intersections in Desmos
Many SAT questions boil down to one idea, two expressions are equal. Instead of solving that equation by hand, Desmos lets you see the exact point where the graphs meet, which is the solution to both rules at once.
The key is to read the right coordinate. Some questions want the full ordered pair, while others only want the $x$ value. This lesson shows how to set up the graphs, click the intersection, and extract the value the question is truly asking for.
A Simple Definition Unlocks Finding Intersections in Desmos
If an equation says $f(x) = g(x)$, you graph $y = f(x)$ and $y = g(x)$. Any intersection point makes both sides equal, so the $x$ coordinate is a solution to the equation.
For a system of two equations in $x$ and $y$, the intersection point gives both values. If the graphs never meet, there is no solution. If they overlap, there are infinitely many solutions.
Work Through Finding Intersections in Desmos Step by Step
Solve $x^2 = 2x + 3$ by finding intersections.
Use intersections to solve $x^2 = 2x + 3$ so you can see both solutions at once.
Graph the first side so you can compare it to the other side.
Graph the second side on the same axes to see intersections.
First intersection gives one solution
Second intersection gives the other solution
Use Desmos to Check Finding Intersections in Desmos
Solve $x^2 = 2x + 3$ by finding intersections.
Graph both equations, click the intersection point, and read the coordinates. If you only need $x$, ignore the $y$ value.
y = x^2
y = 2x + 3
Desmos is faster for messy systems. Algebra is faster for clean integers and simple equations.
Expert move: Graph both equations and click the intersection(s). The $x$-value solves a single equation, and the full $(x, y)$ point solves a system.
Check context: If there is no intersection, you have no real solution; if the graphs overlap, there are infinitely many solutions.
- Desmos features used: intersections.
- Common mistake: reading the wrong coordinate from the intersection.
Practice Finding Intersections in Desmos with SAT-Style Questions
Choose the correct interpretation of intersections.
If two graphs intersect at , what does that mean?
To solve in Desmos, you should graph
A system has two intersection points. How many solutions does it have?
If a line and a parabola intersect once, how many real solutions are there?
Key Takeaways to Remember for Finding Intersections in Desmos
- Intersections solve $f(x) = g(x)$.
- Read the correct coordinate based on the question.
- Desmos is ideal for messy systems.
About the Instructor
