The graph of a quadratic function with vertex (0, 4) is shown in the figure below. Find the domain and the range. 10. 8. 6- -10 10 Write your answers as inequalities, using x or y as appropriate. Or, you may instead click on "Empty set" or "All reals" as the answer. (a) domain: O
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- #6- If you were to graph two quadratic functions on the same xy-plane, how many intersection points could there be? Use examples to explain your thinking(in image)The graph of a quadratic function with vertex (0,-2) is shown in the figure. Find the range and th domain. Write your answers as inequalities, using x or y as appropriate. Or you may instead click on empty set or all reals as the answer.A company finds that if they price their product at $35, they can sell 225 items of it. For every dollar increase in the price, the number of items sold will decrease by 5. 1. What is the maximum revenue possible in this situation? (Do not use commas when entering the answer) 2. What price will guarantee the maximum revenue? $
- 13. Find two numbers whose sum is 98 and whose product is as large as possible.[Hint: Let x and 98−x be the two positive numbers. Their product can be described by the function f(x)=x(98−x).]Formula (quadratic or vertex) needed to apply: ___________________________a quadratic function have a range of (- ∞, ∞)? Justify your answer. b. Discuss the possibilities for the number of times the graphs of two different quadratic functions intersect? c. Discuss the circumstances under which the x-intercepts of the graph of a quadratic function are included in the solution set of a quadratic inequality and when they are14. Find two numbers whose difference is 40 and whose product is as small as possible.[Hint: Let x and x−40 be the two numbers. Their product can be described by the function f(x)=x(x−40).]Formula (quadratic or vertex) needed to apply: ___________________________
- a. Can a quadratic function have a range of (- ∞, ∞)? Justify your answer.b. Discuss the possibilities for the number of times the graphs of two different quadratic functions intersect?c. Discuss the circumstances under which the x-intercepts of the graph of a quadratic function are included in the solution set of a quadratic inequality and when they are not included. No handwritten answers, please. Cannot understand it. ThanksSuppose that Ix - 41 < 1.(a) What is the maximum possible value of Ix+ 41?(b) Show that lx2 - 161 < 9.The speed of a supersonic aircraft is usually represented by a Mach number, named after Austrian physicist Ernst Mach (1838–1916). A Mach number is the speed of the aircraft, in miles per hour, divided by the speed of sound, approximately 740 miles per hour. Thus, a plane flying at twice the speed of sound has a speed, M, of Mach 2. If an aircraft has a speed greater than Mach 1, a sonic boom is heard, created by sound waves that form a cone with a vertex angle θ,, shown in the given figure. The relationship between the cone’s vertex angle, θ,, and the Mach speed, M, of an aircraft that is flying faster than the speed of sound is given by sin θ/2 = 1/M. Solve, If θ = π/6, determine the Mach speed, M, of the aircraft. Express the speed as an exact value and as a decimal to the nearest tenth..
- A highway engineer develops a formula to estimate the number of cars that can safely travel a particular highway at a given speed. She finds that the number N of cars that can pass a given point per minute is modeled by the function N(x) = 88x / 16+16(x/20)^2 use a graphing calculator in the viewing rectangle [0,100] by [0,60] If the number of cars that pass by the given point is greater than 40, at what range of speeds can the cars travel? (Round your values to one decimal place. Enter your answer using interval notation.) mi/ha. Can a quadratic function have a range of (- ∞, ∞)? Justify your answer. b. Discuss the possibilities for the number of times the graphs of two different quadratic functions intersect?c. Discuss the circumstances under which the x-intercepts of the graph of a quadratic function are included in the solution set of a quadratic inequality and when they are not included.A company finds that if they price their product at $ 55, they can sell 171 items of it. For every dollar increase in the price, the number of items sold will decrease by 3. a) What is the maximum revenue possible in this situation? (Do not use commas when entering the answer) b) What price will guarantee the maximum revenue?