Warm-up 1) Solve the system using substitution: 3y - 2x = 11 y + 2x = 9 2) Given the inequality and the graph, shade appropriately.
Application Problem The amount of money that a freshman class fundraiser can raise can be modeled by the inequality y≤-2x2 + 16x – 24, where x represents the number of days into the sale and y represents the amount of money raised in hundreds. a) Graph b) What is the max? What does it represent? c) When will they start to raise money d) How many days should the fundraiser last? e) On which days will the sale make more than $400?
Solving Nonlinear Systems
If the graphs of a system of equations are a conic section and a straight line, the system will have zero, one, or two solutions. Examples no solution 1 solution 2 solutions
You will use these same techniques to solve quadratic systems. We’ve already studied techniques for solving systems of linear equations. You will use these same techniques to solve quadratic systems. These techniques are ??? Substitution, Elimination, Graphing
Find the points of intersection y = x2 +2x+4 & y = 6x + 1 We will use….. Substitution. Now plug these values into the Equation to get y!! (3,19) and (1,7) are the points where the two graphs intersect. Check it on your calculator!
Solve by substitution or Elimination:
A rocket is launched from the ground and follows a parabolic path represented by the equation y = -x2 + 10x. At the same time, a flare is launched from a height of 10 feet and follows a straight path represented by the equation y = -x + 10. When and at what height does the flare and the rocket meet?
A pelican flying in the air over water drops a crab from a height of 30 feet. The distance the crab is from the water as if falls can be represented by the function h(t) = -16t2 + 30, where t is time, in seconds. To catch the crab as it falls, a gull flies along a path represented by the function g(t) = -8t + 15. Can the gull catch the crab before it hits the water? Justify your answer.
Calling All Superheroes This will be your first project. It will be due September 17th at the beginning of class. It will involve not only math but writing and some creativity. Do NOT wait until 16th to try to start and finish this assignment. It will be a quiz grade that will not be replaced by a test.