What is the vertex of the parabola given by = -(x-2)^2-1?

Ily begins solving the equation 4(x – 1) – x = 3(x + 5) – 11. her work is shown below. 4(x – 1) – x = 3(x + 5) – 11 4x – 4 – x = 3x + 15 – 11 3x – 4 = 3x + 4 how can her partial solution be interpreted?

Find the x-intercepts of the parabola withvertex (1,1) and y-intercept (0,-3).write your answer in this form: (x1,if necessary, round to the nearest hundredth.

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .