Finding the equation of a parabola

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In summary, the person is seeking help with a problem involving a parabola and is unsure if derivatives are needed. They have attempted to find a solution using trigonometry but it did not work. They are looking for a hint on how to start the problem and mention the given information of two points with tangents and a y-intercept. They end with a thank you.
  • #1
theBEAST
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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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  • #2
y=ax2+bx+c

You have 2 points where the tangents are given and y intercept.
 
  • #3
azizlwl said:
y=ax2+bx+c

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

Thanks!
 

What is the general form of the equation of a parabola?

The general form of the equation of a parabola is y = ax^2 + bx + c, where a is the coefficient of the squared term, b is the coefficient of the linear term, and c is the constant term.

How do I find the equation of a parabola given three points?

To find the equation of a parabola given three points, you can use the point-slope form of a line to set up a system of equations and solve for the coefficients. Alternatively, you can use the quadratic interpolation method to directly calculate the equation using the coordinates of the three points.

What is the difference between a vertical and horizontal parabola?

A vertical parabola has the equation y = ax^2 + bx + c, where the coefficient a is not equal to 0. This type of parabola opens up or down and has a vertical axis of symmetry. On the other hand, a horizontal parabola has the equation x = ay^2 + by + c, where the coefficient a is also not equal to 0. This type of parabola opens left or right and has a horizontal axis of symmetry.

Can a parabola have a negative coefficient?

Yes, a parabola can have a negative coefficient. In fact, the coefficient a determines the concavity of the parabola. A positive a value results in a parabola that opens up, while a negative a value results in a parabola that opens down.

What is the significance of the constant term in the equation of a parabola?

The constant term, c, in the equation of a parabola represents the y-intercept of the parabola. This is the point where the parabola crosses the y-axis. It can also provide information about the vertex and focus of the parabola when used in conjunction with the other coefficients.

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