Real World Parabola

Parabolas Everywhere

Parabolas and quadratic equations make up a lot of everyday things we use and look at, we just usually are not conscious of it! This is a sign hanging in my living room and there are quite a few parabolas that the cursive writing "love" makes, but I'm just going to focus on one of them!

What Are 2 Easy Ways to Notice Parabolas?

2. It makes a curved "U" shape vertex: (6,0)

point 1: (4,2)

point 2: (8,2)

Equations

Standard Form:

1/2x^2 - 6x + 18

Vertex Form:

y = 1/2 (x - 6)^2 + 0

Questions:

1. What does the minimum height of the parabola represent?

The minimum height of the parabola represents the y value while at it's lowest point.

2. What are the roots and where are they found?

The roots are the two places where the parabola clearly crosses the x axis, they can be called roots, solutions or zeros. In this example, the vertex starts on the x axis, so it only has one solution.

3. What does the maximum height represent?

The maximum height of the parabola represents the y value at it's lowest point.

4. How far away from the start is the "v" in "love" from the start of the parabola?

The vertex is (6,0) so it is 6 away from the start.

5. What is the domain of the parabola, in the letter "V" in "love"?

(negative infinity, positive infinity)

6. What is the range of the parabola, in the letter "V" in "love"?

(6, infinity)