If you take the point on the bridge directly beneath the lowest point on the cable to be the origin, then the parabola has equation
![y = ax^2+bx+10](https://tex.z-dn.net/?f=y%20%3D%20ax%5E2%2Bbx%2B10)
300 ft to either side of the origin, the parabola reaches a value of <em>y</em> = 90, so
![a(300)^2+b(300)+10 = 90 \implies 4500a+15b = 4](https://tex.z-dn.net/?f=a%28300%29%5E2%2Bb%28300%29%2B10%20%3D%2090%20%5Cimplies%204500a%2B15b%20%3D%204)
![a(-300)^2+b(-300)+10 = 90 \implies 4500a-15b = 4](https://tex.z-dn.net/?f=a%28-300%29%5E2%2Bb%28-300%29%2B10%20%3D%2090%20%5Cimplies%204500a-15b%20%3D%204)
Adding these together eliminates <em>b</em> and lets you solve for <em>a</em> :
![(4500a+15b)+(4500a-15b)=4+4 \\\\ 9000a = 8 \\\\ a = \dfrac1{1125}](https://tex.z-dn.net/?f=%284500a%2B15b%29%2B%284500a-15b%29%3D4%2B4%20%5C%5C%5C%5C%209000a%20%3D%208%20%5C%5C%5C%5C%20a%20%3D%20%5Cdfrac1%7B1125%7D)
Solving for <em>b</em> gives
![4500\left(\dfrac1{1125}\right)+15b=4 \\\\ 4+15b = 4 \\\\ 15b=0 \\\\ b=0](https://tex.z-dn.net/?f=4500%5Cleft%28%5Cdfrac1%7B1125%7D%5Cright%29%2B15b%3D4%20%5C%5C%5C%5C%204%2B15b%20%3D%204%20%5C%5C%5C%5C%2015b%3D0%20%5C%5C%5C%5C%20b%3D0)
So the parabola's equation is
![y = \dfrac{x^2}{1125}+10](https://tex.z-dn.net/?f=y%20%3D%20%5Cdfrac%7Bx%5E2%7D%7B1125%7D%2B10)
150 ft away from the origin, the cable is at a height <em>y</em> of
![y = \dfrac{150^2}{1125}+10 = \boxed{30}](https://tex.z-dn.net/?f=y%20%3D%20%5Cdfrac%7B150%5E2%7D%7B1125%7D%2B10%20%3D%20%5Cboxed%7B30%7D)
ft above the bridge.
Answer:
y= -2x-1
Step-by-step explanation:
slope intercept form is y= mx+b
m is the slope or rate
and b is the y intercept and it is where x is zero
to find the slope is rise of run or y/x so your answer is
a
Y intercept = (0, 985)
X intercept = (-197/77, 0)
Answer:-1/12
Step-by-step explanation:
the answer is AB = BC
i just took the test and got it right :))