Sasha and Keoni use their equation (which they call the “short-cut way”) to find the y-value of 3 points: when the x-value is 5, 10 and 437.
For use in a classroom, pause the video and ask these questions:
1. [Pause video at 1:03]. Without using a calculator, how can you determine the value of 25/4?
2. [Pause video at 1:50]. Sasha just wrote that y = 25. What information does that give you about the parabola?
Invite a reluctant or shy student to suggest an x-value on the parabola (just like Keoni suggested x = 437). This is an accessible entry point for students who find contributing to class discussion challenging. Then ask the class to find the y-value for that point by using the equation x = √(4y).
Create an opportunity for productive disagreement by asking students if there is an x-value for which there will be no y-value on the parabola. Some students may think the parabola “ends” at about x = 8.5; others may not conceive of x-values other than whole numbers; and some may understand that there are infinitely many points on the parabola and that x can be any number.
1. What is the y–value of the point on the parabola with the x-value of –7.1?
2. What is the y–value of the point on the parabola with the x-value of √11?