A quadratic function f is given. f(x) = −3x^2 + 6x − 1

(a) Express f in standard form.

(b) Find the vertex and x- and y-intercepts of f. (If an answer does not exist, enter DNE.)

(c) Find the domain and range of f. (Enter your answers using interval notation.)

Aspacecraft can attain a stable orbit 300 kilometers above earth if it reaches a velocity of 7.7 kilometers per second. the formula for a rocket's maximum velocity v in kilometers per second is vequalsminus0.0098tplusc ln upper r, where t is the firing time in seconds, c is the velocity of the exhaust in kilometers per second, and r is the ratio of the mass of the rocket filled with fuel to the mass of the rocket without fuel. find the velocity of a spacecraft whose booster rocket has a mass ratio of 20, an exhaust velocity of 2.1 km/s, and a firing time of 15 s. can the spacecraft achieve a stable orbit 300 km above earth?