SOLUTION: Penelope is out on a Sunday drive in her spaceship. As she approaches Mars, she changes her mind, decides that she does not wish to visit that place, and fires her retro-rocket.

Question 864769: Penelope is out on a Sunday drive in her spaceship. As she approaches Mars, she changes her mind, decides that she does not wish to visit that place, and fires her retro-rocket. The spaceship slows down, and if all goes well, stops for an instant then starts pulling away. While the rocket motor is firing, Penelope�s distance, from the surface of Mars is defined by a quadratic function on the number of minutes since she started firing the rocket. Penelope finds at times 1, 2, and 3 minutes, her distances from Mars are 425, 356 and 293 kilometers, respectively.does your model tell you that penelope crashed into the surface of mars, just touches the surface, or pulls away? defend your answer with mathematical evidence including a sketch of penelope's trajectory (you may use graph paper if it is easier to do so)
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
(1,425); ( 2,356) ; (3,293)
ax^2+bx+c=y
a*1^2+b+c=425,
a*2^2+2b+c=356,
a*3^2+3b+c=293
a = 3, b = -78, c = 500
0=3x^2-78x+500
3/7 (x-13)^2 = 1
She crashed at x = 11.472
min{y = 3 x^2-78x+500} = -7 at x = 13
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