A sandbag was thrown downward from a building. The function f(t) = -16t2 - 32t + 384 shows the height f(t), in feet, of the sandbag after t seconds:

Part A: Factor the function f(t) and use the factors to interpret the meaning of the x-intercept of the function. (4 points)

Part B: Complete the square of the expression for f(x) to determine the vertex of the graph of f(x). Would this be a maximum or minimum on the graph? (4 points)

Part C: Use your answer in part B to determine the axis of symmetry for f(x)? (2 points)

Question

A sandbag was thrown downward from a building. The function f(t) = -16t2 - 32t + 384 shows the height f(t), in feet, of the sandbag after t seconds:

Part A: Factor the function f(t) and use the factors to interpret the meaning of the x-intercept of the function. (4 points)

Part B: Complete the square of the expression for f(x) to determine the vertex of the graph of f(x). Would this be a maximum or minimum on the graph? (4 points)

Part C: Use your answer in part B to determine the axis of symmetry for f(x)? (2 points)

myininaya · Answer

A) You are factoring a quadratic.
 We are going to attempt to factor by grouping.
Find two factors of a*c that have product a*c and sum b.
That is find two factors of -16*384 that have product -16*384 and sum -32.

myininaya · Answer

actually it might make it easier if we start by factoring -16 first.

myininaya · Answer

Then do the whole factor by grouping method.

myininaya · Answer

so what do you get when you factor -16 out ?