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Lesson 4: Developing an Equation for a Parabola Given Any x-Value

Sasha and Keoni use the definition of a parabola, the Pythagorean theorem, and their methods from previous lessons to represent the y-value for any point on a particular parabola given the x-value of that point. In contrast to Lesson 3 in which y-values were given, in this episode x-values will be given.

Episode 1: Making Sense

Keoni and Sasha make sense of the new situation in which the x-value is given and the y-value needs to be determined (instead of the other way around).

Episode 2: Exploring

Keoni and Sasha use the definition of a parabola and the Pythagorean theorem to solve for the y-value of a point on the parabola when the x-value is 5.

Episode 3: Repeating Your Reasoning

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.

Episode 4: Exploring

Sasha and Keoni generalize their “short cut” method from Episode 3 by solving x= √(4y) for y.

Episode 5: Reflecting

Keoni and Sasha compare the equations x = √(4y) and y = x^{2}/4.

Episode 6: Exploring

Keoni and Sasha return to the equation y = x^{2}/4 and derive it using the definition of a parabola, the Pythagorean theorem, and their method from Episode 2.