Use the function f(x) = −16x2 + 24x + 16 to answer the questions. Part A: Completely factor f(x). (2 points)

Part B: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)

Part C: Describe the end behavior of the graph of f(x). Explain. (2 points)

Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph. (4 points)

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Step-by-step explanation:

a) f(x) = -16x^2 + 24x + 16

= -4(4x^2 - 6x - 4)

= -4(2x - 4)(2x + 1)

b) The x-intercepts can be found when y = 0. This happens when

2x - 4 = 0 or x = 2

and

2x + 1 = 0 or x = -1/2

Therefore, the x-intercepts are at (2, 0) and (-1/2, 0)

c) As x approaches positive infinity, f(x) approaches negative infinity. When x approaches negative infinity, f(x) approaches negative infinity. In other words, the graph of this function opens downward.

d) From part (b), we that its graph intersects the x-axis at the 2 points. We also know that it opens downwards. Also, the graph intersects the y-axis at

f(0) = -16(0)^2 + 24(0) + 16

= 16

or at (0, 16)

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