Algebra 2

Where does the water go?

In our everyday world we can find many mathematical ideas used, but very seldom think of the math shown by the picture. One of the most important Algebra 2 ideas is use of quadratic relationships and their graphs.

Attached are a few pictures that show quadratic relationships.

Part 1

  1. In order to find the “equation of the parabola” shown in the picture, we will need to place a grid over the top of the picture.
  1. Now identify any specific points important to finding the equation of the quadratic.
  1. Algebraically determine the quadratic equation that would “fit” the relationship in the picture.
  1. How far is it between the two ends of the water’s path?
  1. What height would we have to go in order to reach the top of the arc?

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Part 2

  1. Find a picture of something that also provides a parabolic shape. You can take a picture of something that shows a parabolic shape or find a picture on the internet. Going to google images, you can find quite a few different pictures that fit the description.
  2. Find the equation that best matches the picture.
  3. Tell me something specific about the picture and its relationship to a parabola. Example: What is the distance to the highest part of the curve to the ground? How far is it between the widest part of the parabolic curve?

Teacher Page

Algebra 2

How far is it to the other end of the rainbow?

In our everyday world we can find many mathematical ideas used, but very seldom think of the math shown by the picture. One of the most important Algebra 2 ideas is use of quadratic relationships and their graphs.

Attached are a few pictures that show quadraticrelationships.

Part 1

  1. In order to find the “equation of the parabola” shown in the picture, we will need to place a grid over the top of the picture
  1. Now identify any specific points important to finding the equation of the quadratic. Students can identify any three points on the parabola to calculate their equation. Many of them will use the vertex and another point. Others will use the x-intercepts and another point.
  1. Algebraically determine the quadratic equation that would “fit” the relationship in the picture.
  1. How far is it between the two ends of the water’s path?
  1. What height would we have to go in order to reach the top of the arc?

If students use the grid that is on the pictures, I have given possible answers for each picture. The equations are in standard form:

y = -2.13x2 + 18.97x – 32.61

Possible equation: y = -0.321x2 + 3x – 2.18

Here is another photo that could be used if you don’t have the time or availability of computer use.

Possible equation: y = -12.92x2 + 145.54x – 405.75

Part 2

  1. Find a picture of something that also provides a parabolic shape. You can take a picture of something that shows a parabolic shape or find a picture on the internet. Going to google images, you can find quite a few different pictures that fit the description.
  2. Find the equation that best matches the picture.
  3. Tell me something specific about the picture and its relationship to a parabola. Example: What is the distance to the highest part of the curve to the ground? How far is it between the widest part of the parabolic curve?