y = ax^2 + bx + 7 because when x = 0 y = 7
when x = -1 y = 14 so we have
14 = a - b + 7
so a - b = 7...............(1)
when x = 1 y = 4
so 4 = a + b + 7
a + b = -3.................(2)
Adding equations (1) and (2) we eliminate b so:-
2a = 4
a = 2
Substitute a = 2 in equation (1)
2 - b = 7
b = -5
so our equation is y = 2x^2 - 5x + 7
![\bf [cot(\theta )+csc(\theta )]^2=\cfrac{1+cos(\theta )}{1-cos(\theta )} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{doing the left-hand side}}{[cot(\theta )+csc(\theta )]^2}\implies cot^2(\theta )+2cot(\theta )csc(\theta )+csc^2(\theta ) \\\\\\ \cfrac{cos^2(\theta )}{sin^2(\theta )}+2\cdot \cfrac{cos(\theta )}{sin(\theta )}\cdot \cfrac{1}{sin(\theta )}+\cfrac{1}{sin^2(\theta )}\implies \cfrac{cos^2(\theta )}{sin^2(\theta )}+\cfrac{2cos(\theta )}{sin^2(\theta )}+\cfrac{1}{sin^2(\theta )}](https://tex.z-dn.net/?f=%5Cbf%20%5Bcot%28%5Ctheta%20%29%2Bcsc%28%5Ctheta%20%29%5D%5E2%3D%5Ccfrac%7B1%2Bcos%28%5Ctheta%20%29%7D%7B1-cos%28%5Ctheta%20%29%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bdoing%20the%20left-hand%20side%7D%7D%7B%5Bcot%28%5Ctheta%20%29%2Bcsc%28%5Ctheta%20%29%5D%5E2%7D%5Cimplies%20cot%5E2%28%5Ctheta%20%29%2B2cot%28%5Ctheta%20%29csc%28%5Ctheta%20%29%2Bcsc%5E2%28%5Ctheta%20%29%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7Bcos%5E2%28%5Ctheta%20%29%7D%7Bsin%5E2%28%5Ctheta%20%29%7D%2B2%5Ccdot%20%5Ccfrac%7Bcos%28%5Ctheta%20%29%7D%7Bsin%28%5Ctheta%20%29%7D%5Ccdot%20%5Ccfrac%7B1%7D%7Bsin%28%5Ctheta%20%29%7D%2B%5Ccfrac%7B1%7D%7Bsin%5E2%28%5Ctheta%20%29%7D%5Cimplies%20%5Ccfrac%7Bcos%5E2%28%5Ctheta%20%29%7D%7Bsin%5E2%28%5Ctheta%20%29%7D%2B%5Ccfrac%7B2cos%28%5Ctheta%20%29%7D%7Bsin%5E2%28%5Ctheta%20%29%7D%2B%5Ccfrac%7B1%7D%7Bsin%5E2%28%5Ctheta%20%29%7D)
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recall that sin²(θ) + cos²(θ) = 1, thus sin²(θ) = 1 - cos²(θ).
Yes. The lines would insert in quadrant 1. At (1,7)
