Homework Help

a soccer ball is kicked from the ground. After travelling 10m, it just clears a...

user profile pic

cassandralivi... | Student, Grade 11 | Honors

Posted July 6, 2013 at 6:59 PM via web

dislike 4 like

a soccer ball is kicked from the ground. After travelling 10m, it just clears a

5 `11/14`  meter tall fence. it strikes the ground 37 meters from the start point. the path is shown below.


express the height of the ball as a function of the distance from the kicking point in factored, vertex and standard form. All constants should be rounded to two decimals

1 Answer | Add Yours

user profile pic

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted July 7, 2013 at 2:36 AM (Answer #1)

dislike 1 like

We have three points: (0,0),(10,`81/14` ),and (37,0).

The three forms of the quadratic equation we are asked to find are:

factored form y=a(x-p)(x-q) where a is a vertical stretch factor, and p,q are the zeros.

standard form `y=ax^2+bx+c`

vertex form `y=a(x-h)^2+k` where a is the vertical stretch factor, and (h,k) is the vertex.

Here y is the vertical height and x the horizontal distance.

(a) Factored form -- we have the two zeros so p=0 and q=37. Then y=a(x-0)(x-37). We can find a using the third point given -- substitute 10 for x and `81/14` for y and we get:

`81/14=a(10)(10-37)`

`81/14=-270a`

`a=(81/14)/(-270)=-3/140`

So the equation we seek is `y=-3/140x(x-37)`

(b) We can expand the product to put in standard form:

`y=-3/140x^2+111/140x`

(c) We can complete the square to put in vertex form:

Factor out the leading coefficient:

`y=-3/140(x^2-37x)`  Add and subtract `(37/2)^2=1369/4`

`y=-3/140(x^2-37x+1369/4-1369/4)`

`y=-3/140((x-37/2)^2-1369/4)`

`y=-3/140(x-37/2)^2+4107/560`

------------------------------------------------------------------

With y the height of the ball as a function of x, the horizontal distance, we have:

factored form: `y=-.02x(x-37)`

standard form: `y=-.02x^2+.79x`

vertex form: `y=-.02(x-18.5)^2+7.33`

All units in meters and fractions rounded to 2 decimal places.

----------------------------------------------------------------

The graph:

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes