Question

) A gigantic gate to the entrance of a theme park in the shape of a parabola is constructed
on a level ground. The horizontal distance between the end points to the gigantic gate is 20 meters. The maximum height of the gigantic gate from the ground is 5 meters. Calculate the height of the gigantic gate at a horizontal distance of 4 meters from one of the end points.

Answer 1

do you have an idea on what type of question you're dealing with?

Answer 2

i have the idea.. the idea is about parabola.. i just want to know that if the solution is long or short because the mark are 10..

Answer 3

any mark count, if you have 40 you'll need 10 to pass remember

Answer 4

yeah i know.. i need help to find the solution of this question

Answer 5

my dear we'll firsyt need to find the equation of this parabola fist

Answer 6

so i need to use y^2=4px

Answer 7

let find the points on the curve, the vertical distance from the ground to the top of the gate is on the Y-axis therefore our parabola cuts Y-axis at 5 get that

Answer 8

yes.. i got that

Answer 9

so you and me knw that the at y-intercept X equals zero right?
but they tol us that from the end of the parabola to the other we have 20 there fore will need 10 to the left(negatives) of Y-axis and 10 the right of Y-axis(positives) therefore therefore the parabola will cut the X-axis at -10 and 10 get that too?

Answer 10

yes.. i also got that..

Answer 11

now i need your attention
the equation of the [parabola is reprented by aX^2 + bX + c = 0 now to find this actual equation in a particular case we need to find a,b and c. that is 3 unknowns, so this means we need 3 pieces of information which are 3 points on the curve. can you recognise the 3 points?

Answer 12

the vertex(0,5), the F(0,0)

Answer 13

we have (0,5) (10,0) and (-10,0) see them?
at Y-int X=0 and aT X-int Y=0

Answer 14

oh. ok2.. understand... then what we need to find???

Answer 15

we need a,b and c
c= y-int which is 5 get that?

Answer 16

no i don't get that.. could you show it to me??

Answer 17

Alright i said that let the equation of the parabola be aX^2 + bX + c = Y
do u knw it? it is the general form of a parabola

Answer 18

so if at y-int x=0.......................that equation becomes : Y=a(0)^2 + b(0) + c therefore Y= c..... meaning c is the Y-intercept got it now?

Answer 19

then the equation becomes Y=aX^2 + bX + 5............... because our y-intercept is 5

Answer 20

to find b remember the formula of the axis of symetry.....X=-b/2a
this is the value of X at the turning point which is zero
.......therefore 0=-b/2a..........times both sides by -2a u'll get b=0

Answer 21

our parabola become Y=aX^2 + 0X +5.... which is Y=aX^2 + 5

Answer 22

to find a we say when x= -10 or x=10 y=0.........if we substitute we'll get 0=a(10)^2 + 5.......u'll get a=-5/100..... which is a=-1/20

Answer 23

so then we use y(x) = ax^2

Answer 24

now since we have a=-1/20 b=0 and c=5 ...........our parabola becomes ............Y=-1/20 X^2 + 0(X) + 5................therefore Y=-1/20 X^2 + 5 this is our parabola

Answer 25

are u fine so far it's time to reveal the answer

Answer 26

yes... i got it... the answer is 3.2

Answer 27

now thy are looking for the height og the gate 4 meters from one of the ends from 10 you take off 4 ull get 6 so this means y equal to what when x=6 if u substitute it in our parabola u'll get Y=-0,05(6^2) + 5 ... therefore y=3,2

Answer 28

very correct if u need more help feel free to ask

Answer 29

thank you very much...

Answer 30

u're welcome