Below is the graph of y = x2 +5. 20- 15 10- -4 -3 -2 -1 2 The area bounded by y = x2 + 5 and the raxis from x = -3 to a = -1 is

9. Which of the following represents a quadratic that is vertically stretched by a factor of 4, translated up 6 units, and right 8 units? a. f(x) = 4(x –- 8)² + 6 8) + 6 b. f(x) = - 4(x – 6)´ + 8 %3D c. f(x) = 6(x + 8) – 4 %3D 2. d. f(x) = 4(x + 8) - 6

27. A rectangular field is to be enclosed with 200 meters of fence. Which of the following models will express the area of the field as a function of one of its sides, say x? a. A(x)=x(100-x) b. A(x)=x(200-x) c. A(x)=x²(100-x) d. A(x)=x(100-x)² e. A(x)=x²(200-x)

The U.S. population can be modeled by the function y=165.6x¹.345, where y is in thousands and x is the number of years after 1800. (a) What was the population in 1970, according to this model? (b) is the graph of this function concave up or concave down? What does this mean? (c) Use numerical or graphical methods to find when the model estimates the population was 94,150,000. (a) According to the model, the population in 1970 was thousands. (Round to the nearest integer as needed.)