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Systems of Equations
Linear Programming
Exponential Functions
What type of FUNction Is It?!
Solving Equations, Inequalities, & Absolute Values
100
Name the 3 methods that we learned to solve systems of equations.
Graphing, Substitution, and Elimination/Combination
100
What is the Feasible Region?
The shaded portion of the graph that indicates the set of all possible combinations.
100
What does the value 'A' tell us about the graph of an exponential equation?
'A' is the y-intercept or start value.
100
How do you determine if a table represents a quadratic relationship?
The second difference in the table will be a constant value.
100
Solve the following equation: 3t + 23 -2t = 18
t = -5
200
How many solutions does a system of parallel lines have?
Zero or No solutions
200
Name the 6 steps of a linear programming problem.
1) Define your variables 2) Write your Objective Function 3) Write your Constraints 4) Graph your Constraints/Feasible Region 5) Corner Principle 6) Answer the question in full sentences
200
How can you determine if an exponential EQUATION is decay or growth?
The 'B' value: If B>1 then exponential growth If 0
200
If the graph of an equation is a straight line, what type of relationship does it represent?: Linear, Quadratic, or Exponential
If the graph of an equation is a straight line, this represents a Linear Equation.
200
Solve the following absolute value equation: |2x-3| = 7
x = -2 and x = 5
300
Solve the following system, using a method of choice: 2x + y = 12 3x - 2y = 11
The solution to the system 2x + y = 12 3x - 2y = 11 is (5,2).
300
Graph the following constraints on a graphing whiteboard: 3x + 4y < 24 y > 0 2x + 2y < 14 x > 0
3x + 4y < 24 y < -0.75x + 6 OR y-intercept: (0,6) x-intercept: (8,0) 2x + 2y <14 y < -x + 7 OR y-intercept: (0,7) x-intercept: (7,0)
300
Graph the following exponential equation on a coordinate whiteboard: y = 2(2^x)
(Graph on Board)
300
Is the following equation Linear, Quadratic, or Exponential? y = 3x(2x-4)
y = 3x(2x-4) is a quadratic equation: y = 6x^2 -12x
300
Solve the following inequality: 7(x-2) > 4x - 23
x >-3
400
At The Apple Pan, two burgers and three orders of fries cost $19.75.  Five burgers and two orders of fries cost $37.   1) Write the system of equations that fit the scenario. 2) What is the cost for a burger? An order of fries?
B-$ of 1 burger F-$ of 1 order of fries 1) 2B + 3F = 19.75 5B + 2F = 37 2) One burger costs $6.50 One order of fries costs $2.25
400
Write the objective function AND constraints for the following scenario: Bob builds tool sheds. He uses 10 sheets of dry wall and 15 studs for a small shed and 15 sheets of dry wall and 45 studs for a large shed. He has available 60 sheets of dry wall and 135 studs. If Bob makes $390 profit on a small shed and $520 on a large shed, how many of each type of building should Bob build to maximize his profit?
L = # of Large Sheds S = # of Small Sheds f(S, L)= 390S + 520L 10S + 15L <= 60 (Sheets of Drywall) 15S + 45L <= 135 (Studs)
400
Write the equation for the following table: X Y -1 2 0 6 1 18 2 54 3 162
y = 6(3)^x
400
Determine if the following table represents a Linear, Quadratic, or Exponential relationship: X Y -2 3 -1 2 0 2 1 3 2 7
The table represents a quadratic relationship.
400
Solve and graph the following compound inequality: -8 < 5x + 2 < 17
-2 < x < 3 (See board for graph)
500
Rasual says that (4,3) is the solution to the following system. Jamie says that Rasual is wrong and that (3,4) is the correct solution. Explain who is right; if neither of them are correct, determine the correct solution. x + 2y = 10 2x + 3y = 16
Neither of them are correct. The correct solution is (2,4)
500
How do you know if a problem is a systems problem or a linear programming problem?
(Answers)
500
Write the equation for the following table? What is the growth/decay rate? X Y 2 32 3 64 4 128
y = 8(2)^x The GROWTH rate is 100% (2-1)x100% = 100%
500
Sketch an example of all 3 of the following: A linear equation A quadratic equation An exponential equation
(Answers on the board)
500
Who is Mr. Fox's favorite current NBA player?
Carmelo Anthony