i really need help with my math. sos
find an equation that describes the path of a kick that covers a horizontal distance of 20 yards and reaches of maximum height of 9 yards
By the way general formula (height reached = H, distance covered = W, and ball kicked from origin in positive x direction):
y = (-4H/W2) x2 + (4H/W) x = (-4H/W2) x (x - W)
For W = 20 and H = 9 you get y = (-36/400) x2 + (36/20) x = (-9/100) x2+(9/5) x = (-9/100) x (x-20)
Just like Robert's answer.
This question is designed to test shifting and scaling. It is a great question that applies to physics and real life.
You can start off with y=x^2. This gives you a generic U shaped graph.
To flip graph, make X negative...y=-x^2
To make this graph display the max height of 9, you would shift the graph upward by subtracting 9 from y... y-9=(-x^2)...y=(-x^2)+9
Now to get a distance of 20 you would stretch the graph, you do this by multiplying or dividing x by a number.
To find the number(we can use "c") I put the desired points into the equation.. 0=(c*-10^2)+9...c=.09
Now we plug c into the equation...y=(-.09x^2)+9
This equation displays the flight of the kick.
The last step is to set the graph to start at the origin.To do this we must shift the graph to the right. We do this by subtracting 10 from x... y=[-.09(x-10)^2]+9
This may seem like a long process but I tried to go slow. Basically you shift and scale(strech/squeeze) you graph by manipulating you equation just as I did.
Shift up/down...subtract/add to y
Shift right/left...subtract/add to x
Stretch/squeeze... multiply factor to x ... this is the hardest part for me. I usually find the factor to multiply by plugging in desired points.
Since the projectile path is a parabola, you can let y = a(x)(x-20)
Plug in (10, 9) to solve for a, (since the peak is at the middle.)
9 = a(10)(-10)
a = -9/100
Answer: y = -(9/100)(x)(x-20)