Javier throws a ball to his friend(who misses the catch). The height of the ball h(x) in feet can be modeled by the function h(x)=-0.8(x+1.185)(x-6.035) where x is the ball's horizontal distance in feet from where it was thrown. a. Algebraically determine the horizontal intercepts of the function and explain their meaning in the context of the problem. b. Algebraically convert this formula to standard form by distributing and combining like terms. c. state the vertical intercept of the function and explain its meaning in the problem context.

A farmer wants to fence an area of 24 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. Let y represent the length (in feet) of a side perpendicular to the dividing fence, and let x represent the length (in feet) of a side parallel to the dividing fence. Let F represent the length of fencing in feet. Write an equation that represents F in terms of the variable x. F(x) = Find the derivative F'(x). F'(x) = Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) X = What should the lengths of the sides of the rectangular field be (in ft) in order to minimize the cost of the fence? smaller value ft larger value ft Submit Answer

For the function y = 3x2 + 9x + 4, at the point x = 8, find the following.

The per capita (per person) income from 1985 to 2010 can be modeled by f(x) = 2000(x- 1985) + 15,000 where x is the year. Determine the year when the per capita income was $23,000. The per capita income was $23,000 in the year

The worldwide sales in millions of hand-held PCs can be modeled by the function P(x) 1.85(x 1998) + 4 where x is the year. Use the function to determine the year when sales reach $25 million.

“e” was very happy as he was going to six flags. He pictured the perfectroller coaster and wondered what the equation of such a perfect roller coaster would be. Atsix flags, he discovered the following equation:h(d) = d3-7d2+8d+1where h (d) represents the vertical height above the ground and d represents the horizontal distance the roller coaster has travelled.Using calculus methods only, sketch the function by stating all the following:o Any asymptotes o The y-intercept o The first and second derivative o All critical points and whether they are the maximum, minimum, or neither. o All inflection points and the concavity to the left and right of the points o Graph Show all your work

x2 + 6x + 8, 7. For the graph of the function f(x) A. Write the function in standard form: B. find the vertex; C. x-intercepts D. y-intercepts E. Graph the function

2) Given the function g(x) = 4x²-16 2x+7 a. Use evaluation and function notation to determine the vertical intercept. b. Set up an equation and determine the horizontal intercept(s) of the function. c. Simplify the expression g(a + 2).