Solving equations by graphing: intro | Algebra 2 | Khan Academy

Name: Solving equations by graphing: intro | Algebra 2 | Khan Academy
Uploaded: 2019-07-22T17:52:33.000Z
Duration: 4 min 27 s
Channel: Khan Academy
Description: - 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 =

July 22, 2019

Khan Academy

TL;DR

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

Transcript

[Instructor] We're told, this is the graph of y is equal to 3/2 to the x. And that's it right over there. Use the graph to find an approximate solution to 3/2 to the x is equal to five. So pause this video and try to do this on your own before we work on this together. All right, now let's work on this. So they already give us a hint of how to so... Read More

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.

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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.

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Transcript

[Instructor] We're told, this is the graph of y is equal to 3/2 to the x. And that's it right over there. Use the graph to find an approximate solution to 3/2 to the x is equal to five. So pause this video and try to do this on your own before we work on this together. All right, now let's work on this. So they already give us a hint of how to so... Read More

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.

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.