Finding the equation of a parabola

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SUMMARY

The discussion focuses on finding the equation of a parabola given two points with tangents and a y-intercept. The standard form of the parabola is expressed as y = ax² + bx + c. The user initially attempted to apply trigonometric relationships but found them unsuitable due to the curvature of the parabola. The key takeaway is that understanding the properties of parabolas and their derivatives is essential for solving such problems.

PREREQUISITES
  • Understanding of quadratic equations and their standard form (y = ax² + bx + c)
  • Basic knowledge of calculus, specifically derivatives
  • Familiarity with the concept of tangents to curves
  • Ability to interpret graphical representations of functions
NEXT STEPS
  • Study the derivation of the quadratic formula and its applications
  • Learn how to find the derivative of a quadratic function
  • Research methods for determining the equation of a curve from given points and tangents
  • Explore graphical methods for visualizing parabolas and their properties
USEFUL FOR

Students studying algebra and calculus, educators teaching quadratic functions, and anyone seeking to understand the geometric properties of parabolas.

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Homework Statement


Alright so I wasn't sure if I should put this in the Calculus section, but just in case that I would need derivatives to solve this I decided I would put this thread here.

http://img99.imageshack.us/img99/9351/capturepf.png

The Attempt at a Solution


I tried finding the relationship with trigonometry but it didn't work because the parabola is curved and does not extend as a straight line like a triangle. Could anyone give me a hint on how to start this question?
 
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y=ax2+bx+c

You have 2 points where the tangents are given and y intercept.
 
azizlwl said:
y=ax2+bx+c

You have 2 points where the tangents are given and y intercept.

Thanks!
 

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