Write a quadratic function in vertex form that contains vertex (1,2) and point (-2,8)

Alex drew a circle with right triangle prq inscribed in it, as shown below: the figure shows a circle with points p, q, and r on it forming an inscribed triangle. side pq is a chord through the center and angle r is a right angle. arc qr measures 80 degrees.

Hurry im being timed the graph of f(x)=x^3-3x^2+4 is shown based on the graph how many distinct real numbers solutions does the equation x^3-3x^2+4=0 have

The volume of a spherical hot air balloon v(r) = 4 3 ? r3 changes as its radius changes. the radius is a function of time given by r(t) = 3t. find the instantaneous rate of change of the volume with respect to t at t = 2.