Finding the equation of a parabola (1 Viewer)

[****alyssa****]

Hi! ^_^ I'd realy appreciate some help on this question

Its an upside down parabola, and intersects the x axis at 5, and the y axis at 10. It also gives me the angle of inside the curve measured from the y axis up, as 70 degress, but i don't get how thats relevant How would I find the equation? It seems so simple but I've been through my whole textbook and i can't find another question like it I think i find the gradient by differentiating, but I don't know if thats right or where to go from there

 

[Riviet]

What's the exact wording of the question?

 

[****alyssa****]

lol i didn't think i explained it well enough heres what it looks like, its got a domain restriction on it i guess since it doesn't look like a normal parabola ;]

http://i4.tinypic.com/23qxm40.gif

it's not a worded question, just says find the equation of the parabola, and gives the sketch of it thanks for replying

 

[Sober]

f(x) = ax² + bx + c

You have three conditions to meet, they can be written as:

(1) f(0) = 10
(2) f(5) = 0
(3) f'(0) = -tan(20º)

Using (1):
0a + 0b + c = 10
c = 10

Using (3)
f'(0) = 2a*0 + b = -tan(20º)
b = -tan(20º)

Using (2)
25a + 5b + c = 0
25a - 5tan(20º) + 10 = 0
a = (tan(20º)-2)/5

Therefore:

f(x) = (tan(20º)-2)*x²/5 - tan(20º)*x + 10

 

[****alyssa****]

wow thanks sooooo much guys :O

i don't understand though why you use tan? like what's the relationship between it and the angle... it's just stumped me coz i've never done anything with angles in a parabola :/

 

[****alyssa****]

i totally get it! :O like it makes so much sense and ive been so confused about it for so long >.< thanks for taking the time to explain it ;]