Question 4 Essay Worth 10 points) (07.03, 07.05 HC) 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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raphealnwobi raphealnwobi · Answer 1 · 2022-03-28T13:25:51+02:00

The factored form of the function is f(x) = -8(x - 2)(x + 1), the x intercept is x = 2; and x = -1/2

A parabola is a plane curve with a u shape. The equation for a parabola is in the form of a quadratic equation, that is:

y = ax² + bx + c

If a is positive, the parabola faces up whereas if a is negative, the parabola faces down.

a) From the equation:

f(x) = -16x² + 24x + 16

f(x) = -8(2x² - 3x - 2)

f(x) = -8(x - 2)(x + 1)

b) The x intercept is at f(x) = 0, hence:

0 = -8(x - 2)(2x + 1)

x - 2 = 0; and 2x + 1 = 0

x = 2; and x = -1/2

c) Since a is negative, hence the graph faces down

d) The graph of the function is plotted and attached.

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