Solving equations by graphing: intro | Algebra 2 | Khan Academy | Summary and Q&A

TL;DR

Use the graph of an equation and its intersection with a second equation to approximate the solutions to the original equation.

Key Insights

• 😥 Graphing equations and finding the intersection points is an effective method to approximate solutions.
• 👈 The x-values at the intersection points of two graphs represent solutions to the original equation.
• #️⃣ The number of times two graphs intersect indicates the number of solutions to the equation.

Transcript

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Questions & Answers

Q: How can graphing be used to approximate solutions to equations?

By graphing the given equation and setting it equal to another equation, we can find the x-values where the graphs intersect, which give us the approximate solutions to the original equation.

Q: What does it mean if two graphs intersect at a certain point?

If two graphs intersect at a specific point, it means that the corresponding x-value and y-value satisfy both equations simultaneously, indicating a solution to the original equation.

Q: How can we determine the number of solutions to an equation using graphing?

By graphing the equation and counting the number of times the graph intersects with a specific line, we can identify the number of solutions to the equation.

Q: Are the approximate solutions obtained through graphing always exact?

No, the approximate solutions obtained through graphing may not be exact, but they provide a close approximation to the actual solutions of the equation.

Summary & Key Takeaways

• By graphing the equation y = 3/2^x and setting it equal to the right-hand side, y = 5, we can find the approximate solution for 3/2^x = 5, which is x ≈ 4.

• Graphing the equation y = x^3 - 2x^2 - x + 1 and setting it equal to y = -1 helps determine the number of solutions for x^3 - 2x^2 - x + 1 = -1, which is three.

• Setting y = 2 and graphing it with y = x^3 - 2x^2 - x + 1 shows that x^3 - 2x^2 - x + 1 = 2 has only one solution.