Can Geometry and Algebra Explain a Triangle's Romance with a Parabola?

In summary, the conversation discusses a problem involving a parabola and a triangle, where the goal is to find the base and height of the triangle. The participants suggest drawing a diagram and trying different values of a, such as 4 and -1/2. They also discuss equations involving the parabola and determine that the base of the triangle can be found by solving for the intersection of the parabola and a line. They also make a correction to the diagram and suggest using the X2 button for exponents.
  • #1
crouch88
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  • #3
All you have to do is figure out the base and height of the triangle. Can you find where the parabola intersects the line? Are there some values of a that don't work? It might help to draw a picture as an example. Try a = 4. Also try a = -1/2.
 
  • #5
okay okay wait wait...

I solve y=a(squared) and y=9*x(squared) - a --- to get two equations
Also when x=0 for the parabola, y=-a right?

Uh okay...could you tell me then what I should do?

OHHH I made a mistake in the diagram...y is not -0.3 ... y=-3
 
  • #6
crouch88 said:
okay okay wait wait...

I solve y=a(squared) and y=9*x(squared) - a --- to get two equations
Also when x=0 for the parabola, y=-a right?

Uh okay...could you tell me then what I should do?

OHHH I made a mistake in the diagram...y is not -0.3 ... y=-3

Use the X2 button to do superscripts. So what did you get when you solved

y = 9x2 - a and y = a2?

Can you figure out the base of the triangle and its height?
 

Related to Can Geometry and Algebra Explain a Triangle's Romance with a Parabola?

1. How is it possible for a triangle and a parabola to get romantic?

In mathematics, objects such as triangles and parabolas are used to represent different concepts and relationships. In this case, the triangle and parabola are being used as a metaphor for a romantic relationship. The question itself is not meant to be taken literally, but rather to explore the connection between these two shapes.

2. What is the significance of using a triangle and a parabola in this scenario?

The triangle and parabola have specific properties and characteristics that can be used to describe different aspects of a romantic relationship. For example, the triangle can represent the three key elements of a relationship - love, trust, and communication, while the parabola can represent the ups and downs or curveballs that can occur in a relationship.

3. Can this metaphor be applied to other types of relationships?

Yes, the triangle and parabola metaphor can be used to describe any type of relationship, not just a romantic one. The triangle can represent the different components of any relationship, while the parabola can represent the journey and challenges that come with it.

4. How does this metaphor relate to mathematics?

In mathematics, shapes and equations can be used to represent and explain real-world situations. In this case, the triangle and parabola are being used as symbols to represent the complexities and dynamics of a relationship. This metaphor highlights the versatility and applicability of mathematical concepts.

5. Is there a deeper meaning behind this metaphor?

The deeper meaning behind this metaphor is open to interpretation and can vary from person to person. Some may see it as a way to explore the emotional and psychological aspects of a relationship, while others may view it as a creative way to understand mathematical concepts. Ultimately, the meaning behind this metaphor depends on the individual's perspective and understanding.

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