 # 1. Determine the vertex of the quadratic function f(x) =-x²+2...

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1. Determine the vertex of the quadratic function f(x) =-x²+2x+5. Show some work. 2. Find the x-intercepts of -2x2 10x 3. Write the equation of the quadratic function in standard form that has avertex of (1, -2) and passes through the point 14). 4 Write polynomial thathas the following zeros with the given multiplicities. Do not expand the function -2 with multiplicity 2,3 with multiplicity 3,and 4 with multiplicity 1. 5. Describe the long range behavior of the function f(x) (x*-6x²-x+10) 6. Find all the real zeros of f(x)= x4 -x³ 20x2 Be sure to list the multiplicity of each. 7. Consider the following function: g(x)===((x+2)^(3x-5)° each a. Determine the (-intercepts for g(x) and describe what g(x) is doing at each intercept (tangent, crossing, etc.). Describe the long-range behavior of g(x) Determine the y-intercept for g(x) 5(x2-4) 8. Consider the following rational function: g(x)= List each of the following x²+2x-8 each vertical asymptotes (if they exist) horizontal asymptote (if exists) holes any exist) d. <-intercept -intercept 9. Find the slant asymptote of f(x): 2x2-8 10. The cost Cof producing units of a product is given by C = 0.2x² +10x+5 and the average cost per unit is given by C= C 0.2x²+10x+5 x>0 x Sketch the graph of the average cost function, and estimate the number of units that should be produced to minimize the average cost per unit. it 11. Give an explanation of why there cannot be fourth-degr ee polynomial with exactly three real zeros and a positive leading coefficient the real zeros are unique 12. Can there be fifth-degree polynomial with three real zeros anda positive leadir ng coefficient? If so, give an example. 13. The population P of Germany (in thousands) from 1999 through 2009 can be modeled by each P(t) -8.87t² -271 41- 80.362. 95t<19 where is the year, with - 9 corresponding 1999. According to the model. in what year did Germany have its greatest population? What was the population? According to the model. what will Germany's population be in the year 2100? Is this result reasonable? Explain. x3+2x²+4 Give an explanation of why the rational function f(x) does not have: vertical 2x°+ each asymptote Does the function have a horizontal asymptote? Does the function have any type of asymptote? If so what type and what that asymptote?

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