# Parabolas Lesson 3

### Developing an Equation for a Parabola for Any Given y-Value

Keoni and Sasha create a general method for representing the x-value for any point on a particular parabola, given the y-value of that point. By using their previous results, along with the Pythagorean theorem, they are able to determine the equation for the parabola.

##### Episode 1: Making Sense

Sasha and Keoni grapple with how to represent a general point on the parabola and how to express different distances involving that point.

##### Episode 2: Exploring

Keoni and Sasha develop an equation that relates the x-value to the y-value for a general point on a particular parabola.

##### Episode 3: Reflecting

Keoni and Sasha reflect on the meaning of their equation.

##### Episode 4: Repeating Your Reasoning

Keoni and Sasha determine the x-value of a point on the parabola with a y-value of 3.5.

##### Episode 5: Reflecting

Sasha and Keoni share ideas about the usefulness of the equation
x = √(4y), which they derived in Episode 2.