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

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The discussion revolves around solving a geometry problem involving a triangle and a parabola. Participants suggest starting by drawing both shapes to identify the triangle's base and height. They discuss finding the intersection points of the parabola and the line, experimenting with different values of 'a' to see which work. There are mentions of solving equations related to the parabola and correcting mistakes in the diagram. The conversation emphasizes the importance of visual representation and mathematical equations to find the solution.
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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.
 
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
 
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?
 

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