## kandsbbf Group Title You live near a bridge that goes over a river. The underside of the bridge is an arch that can be modeled with the function y = –0.000471x² + .837x where x and y are measured in feet. How high above the river is the bridge (the top of the arch)? How long is the section of bridge above the arch? The bridge is about 1,777.07 ft. above the river, and the length of the bridge above the arch is about 888.54 ft. The bridge is about 371.85 ft. above the river, and the length of the bridge above the arch is about 1,777.07 ft. The bridge is about 371.85 ft. above the river, and the length of the bri one year ago one year ago

1. kandsbbf Group Title

The bridge is about 1,777.07 ft. above the river, and the length of the bridge above the arch is about 888.54 ft. The bridge is about 371.85 ft. above the river, and the length of the bridge above the arch is about 1,777.07 ft. The bridge is about 371.85 ft. above the river, and the length of the bridge above the arch is about 888.54 ft. The bridge is about 1,777.07 ft. above the river, and the length of the bridge above the arch is about 371.85 ft.

2. kandsbbf Group Title

plss help???

3. campbell_st Group Title

ok... to find the distance spanned by the arch you need to solve it so $-0.00047x^2 + 0.837x = 0... or... -x(0.00047x - 0.837)$ so x = 0 or 0.837/0.00047 the distance between the points will be the distance spanned. |dw:1358113884987:dw|

4. campbell_st Group Title

ok... do you know to differentiate..?

5. kandsbbf Group Title

no lol what is that?

6. campbell_st Group Title

ok... do you know how to find the line of symmetry of the curve...?

7. kandsbbf Group Title

no

8. campbell_st Group Title

what answer did you get got the distance spanned by the bridge..?

9. kandsbbf Group Title

1,780.851

10. kandsbbf Group Title

@campbell_st

11. campbell_st Group Title

oops missed a digit it should be 0.837/0.000471 and you should get 1777.07

12. campbell_st Group Title

ok so the parabola is symmetric and the highest point of the arch is on the line of symmetry... do you know how to find the line of symmetry..?

13. kandsbbf Group Title

is it the line that goes down the middle?

14. campbell_st Group Title

thats it...

15. kandsbbf Group Title

so how do i figure it out?

16. campbell_st Group Title

ok... so find half the distance spanned by the arch... then substitute that value into the equation for the bridge... that will give the height does that make sense..

17. kandsbbf Group Title

soooo divide 1777.07 by 2?

18. campbell_st Group Title

yep... then substitute it... the highest point is at the centre of the acrch

19. kandsbbf Group Title

which equation?

20. campbell_st Group Title

the original equation 0.000471x^2 + 0.837x

21. kandsbbf Group Title

okay so when i divided it by 2 i got 888.535..... which number do i sub that for in the equation?

22. campbell_st Group Title

thats correct...

23. kandsbbf Group Title

so do i sub that in for x?

24. campbell_st Group Title

yes so its $-0.000471\times(888.535)^2 + 0.837\times888.535$

25. kandsbbf Group Title

so it's D

26. campbell_st Group Title

what did you get for the height..? the length is 1777.07

27. kandsbbf Group Title

371.85

28. campbell_st Group Title

ok... which answer has height 371.85 and length 1777.07

29. kandsbbf Group Title

B

30. campbell_st Group Title

thats it.. well done

31. kandsbbf Group Title

did we answer the last part of the question? How high above the river is the bridge (the top of the arch)? How long is the section of bridge above the arch?

32. campbell_st Group Title

yes... you have all the answers you need height = 371.85 and length 1777.07