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- The cost function for a certain company is C=60x+300 and the revenue is given by R=100x0.5x2. Recall that profit is revenue minus cost. Set up a quadratic equation and find two values of x (production level) that will create a profit of $300.A box shaped like a block is used to make a place to plant potatoes. The box will be made using cardboard. If the width of the box is 10 cm more than the longest diameter of the potatoes planted and the height of the box is x cm, then so that the box can contain the largest possible potato, determine the height, length and width of the box. Explain your settlement strategy in full. (2 potatoes= 17cm) with quadratic functionYour R&D department is testing the falling pattern for a new shell to be used for artillery. To perform this test your team tosses a test shell off the edge of a cliff towards a river. Molly, a mathematician team member, was observing and obtained a digital picture of this fall. Using her mathematical knowledge, Molly modeled the shell’s fall with the following quadratic functions: h(t)=-16t2+32t+48 h(t)=-16(t+1)(t-3) h(t)=-16(t-1)2+64 Why does Molly have three equations? Could you convince others that all three of these rules are mathematically equivalent? Which of the forms would be most helpful in answering questions D-F? Explain. What is the maximum height the shell reaches and when will it occur? Show work to support your answer. When would the shell splash into the river? Show work to support your answer. At what height was the shell when it was tossed off the cliff? Show work to support your answer.
- Determine maximum or minimum income, earnings and investments through the vertex of a quadratic equation. Mrs. Miranda has a business selling cookies and biscuits. When you sell "x" items per year, the income is described by the quadratic function: f(x)= 72x – 0.08x2 1. Calculate the number of items you should sell each year for maximum income. 2. What is the maximum income?The quadratic model for the cost in Php of manufacturing computer parts is C(x) = x^2 - 6x + 20. Where x is the number of computers the company manufactures. How much is the cost if the number of computers (x) are 10, 50, 100, and 250? Show the complete solution and find the: a. Graph and the Description of Opening (Stretched or Shrunk) b. Concavity (Opening Upward or Downward) c. y-Intercept and x-intercept/s d. Roots and Nature of Roots (Real, Repeated, or Imaginary) e. Extremities (Vertex – h,k) and Description (Maximum or Minimum) f. Axis of Symmetry, Domain, RangeAn amusement park is building a roller coaster with a drop section modeled by a quadratic. The roller coaster will dip 8 feet below ground level. The roller coaster will dip below ground level at a horizontal distance of 46 feet from the peak re-emerge to ground level at a horizontal distance of 74 feet from the peak.What is the expression that models this scenario? (Use the peak of the roller coaster, just before the drop section, as your y-intercept)
- Rewrite the following quadratic function y = x2 + 2x – 77/22 in vertex form by completing the square. State the vertex, the axis of symmetry, the minimum or maximum value, the x- and y-intercepts, the domain, and the range. Sketch the graph. Answer Step-by-steps. Rewrite the following quadratic function y = 2x2 – 18x + 28 in vertex form by completing the square. State the vertex, the axis of symmetry, the minimum or maximum value, the x- and y-intercepts, the domain, and the range. Sketch the graph. Answer Step-by-steps.I have a question the cost for producing xitmes is 40x+300 and the revenue for selling x itmes is 80x-05x^2 the profit that the company makes is how much it spends(cost). part a. set up an expression for the profit from the producing and selling x items. We assume the company sells all of the items that it produces. (hint it is a quadratic polynomial.) part b. find 2 values of x that will create a profit of $50. part c is it possible for the company to make a profit of $2,500Fred, Elena, Michael, and Diane visit a roller coaster. Elena snaps a picture of part of the coaster from the park entrance. The diagram below represents this part of the coaster. Do you think quadratic, cubic, or quartic function would be the best model for this part of the coaster? Clearly explain your choice.
- Q2 Please help with parts a and b (a) Solve below polynomial function by factoring: 2x2 + 38x - 84 = 0 (b) Graph abobe polynomial function after solving it.1. Fill in the blanks to complete the story that models this quadratic function. An angry bird is shot into the sky which can be modeled by the function h(t)=−0.2t2+1.3t+15h(t)=-0.2t2+1.3t+15 where _______ is height in feet and ______ is time in seconds. Write the sentence and fill in the blanks with the appropriate words. For each of the following, answer the question and describe your reasoning. 2. Write the variables as an ordered pair. ( ____, ____ ) 3. How high above the ground was the bird when it was launched? 4. What is the height of the angry bird at its highest point. 5. When will the angry bird be at a height of 3 feet? 6. Graph the function, label the axis, and name the graph. 7. List two different types of examples of non-quadratic equations.Find the x intercept of quadratic using quadratic formula and find the y intercept of quadratic write both intercept as a coordinate point and show all your work and make sure handwriting is nice no cursive.