Just for Fun – Visualizing Area Relationships for the Standard Vertex Form Equation of the Parabola | Steve Wait – October 28, 2021

For a point P_(x,y) on the Parabola in the standard vertex form y = x², the area x² equals the area of product y and the length of the Latus Rectum.

${y}={{x}}^{2}$

$1^{1}\times {{y}}^{1}=\left(1^{1}\times {{x}}^{1}\right)\times \left(1^{1}\times {{x}}^{1}\right)$

$x=.5$

$1^{1}\times {{y}}^{1}=\left(1^{1}\times {.5}^{1}\right)\times \left(1^{1}\times .5^{1}\right)$

$1^{1}\times {{y}}^{1}={.5}^{1}\times {.5}^{1}$

${{y}}^{1}=\frac{\left({.5}^{1}\times {.5}^{1}\right)}{1^{1}}$

${{y}}^{1}=\frac{{.5}^{2}}{1^{1}}$

${{y}}^{1}=\frac{{.25}^{1}}{1^{1}}$

${{y}}^{1}={.25}^{1}$

$y=.25$

 

A GeoGebra animation can be viewed here: Area Relationships of the Parabola – GeoGebra