Determining the equation of a parabola

[djsandals]

Today we had the last part of the Applications SAC, and I understood most of it, except for one question which was worth 5 marks.

It was a "show that" question  where we had to find the equation of a parabola where we knew the gradient at the first point, the first point and another point.

I talked to a lot of people who struggled with this question also, how do you determine the equation of a parabola given only this information?

Thanks

[tram]

Start with the general equation of

You need to solve for three unknowns and hence need three equations.

You can get two of the equations from subbing the two known points in. You get the third equation by differentiating the general equation, then subbing in the gradient and x-value of the first point.

Hope that help

EDIT: latex added, thanks for the tip b^3!

[djsandals]

Thankyou