Question

5. You can tell a lot about an expression without doing any computation. For example, the expression 16(5+t)(17-t) can be used to model how high a toy rocket is in the air after t seconds. a. Describe the expression. b. When is the value of the expression negative? Explain how you know. c. What does it mean for the expression to be negative in terms of the rocket?

Answer 1

a. The expression 16(5+t)(17-t) is a quadratic polynomial with a negative leading coefficient. It represents a downwards opening parabola. Further, since -5 and 17 are the zeros of the polynomial, hence the line of symmetry is y = (17+5)/2 or, y = 11. The vertex lies on this line.

b. Since t = 0 or, t > 0, the expression is 16(5+t)(17-t) will be negative if 5+t > 0 and 17- t < 0 , i.e. if t > 17.

c. When the expression is 0, the rocket is on the ground, after falling. Since it cannot go below the ground, there is no meaning of the expression being negative.