Activity
Access the Desmos guide PDF for tips on solving problems with the Desmos graphing calculator.
Here is an example of an equation being solved by graphing and by completing the square.
Verify: is approximately 1.414. So and .
For each equation, find the exact solutions by completing the square and the approximate solutions by graphing. Then, verify that the solutions found using the two methods are close. If you get stuck, refer back to the example.
1.
a. Find the exact solutions by completing the square.
Compare your answer:
b. Graph the equation to find approximate solutions.
Use the Desmos graphing tool or technology outside the course.
Compare your answer:
c. Are the solutions you found using the two methods close?
Yes. Solutions were the same: and .
2.
a. Find the exact solutions by completing the square.
Compare your answer:
b. Graph the equation to find approximate solutions.
Use the Desmos graphing tool or technology outside the course.
Compare your answer:
c. Are the solutions you found using the two methods close?
Yes. Solutions were the same: and .
3.
a. Find the exact solutions by completing the square.
Compare your answer:
b. Graph the equation to find approximate solutions.
Use the Desmos graphing tool or technology outside the course.
Compare your answer:
c. Are the solutions you found using the two methods close?
Yes. Solutions were the same: and .
4.
a. Find the exact solutions by completing the square.
Compare your answer:
b. Graph the equation to find approximate solutions.
Use the Desmos graphing tool or technology outside the course.
Compare your answer:
c. Are the solutions you found using the two methods close?
Yes. Solutions were the same: and .
Are you ready for more?
Extending Your Thinking
What quadratic equation of the form would have the solutions and ?
Enter the quadratic equation.
Compare your answer:
. Working backward, these are solutions to . In standard form, this is .
Self Check
Additional Resources
Using the Calculator for Approximate Solutions
Let's look at the solutions to the equations from 9.5.2: Additional Resources:
A more compact way to write the two solutions to the equation is: .
How large or small are those numbers? Are they positive or negative? We can use a calculator to compute the approximate values of both expressions:
or
We can also approximate the solutions by graphing. The equation is equivalent to , so we can graph the function and find its zeros by locating the -intercepts of the graph.
Try it
Try It: Using the Calculator for Approximate Solutions
Approximate the solutions to .
Here is how to approximate the solutions:
Step 1 - Write two expressions.
Step 2 - Use the calculator to approximate the solutions to three decimal places.