Linear Functions
What is the slope of the line that passes through the point (-1,3) & (4, -9)
-12/5
1) No solution
2) One unique solution
3) Infinitely many solutions
1) A Number ≠ 0
2) A Variable = A Number
3) 0 = 0
What is the Rate of Change Formula?
will accept (y1-y)/(x1-x)
Daily Double!!
If b2-4ac is less than 0 what must be true about the graph?
It has no "Zeros" or it does not cross the X-Axis
f(x) = 4x7+13x4-5x3+7
Identify the:
Degree
Leading Term
Leading Coefficient
Degree: 7
Leading Term: 4x7
Leading Coefficient: 4
Write an Equation with a Slope of 13 and Y-Intercept of -2
f(x)=13x-2
Set Up this system of equations (You do not need to Solve it)
The Carnival has a wheel spinning game and a dunk tank. The wheel costs $5 per game and the dunk tank costs $7 per game. The carnival made a total profit of $226. 40 games were played in total.
Use W for the Wheel and D for the Dunk Tank.
5W+7D = 226
W + D = 40
f(x) = -4x+5
What is the Average Rate of Change of f(x) at the interval
[3,4]
Hint: What kind of function is f(x)?
-4
Slide 3
Hint: Use the Quadratic Formula
100 Bonus Points
2) Reduce/Simplify your answer
Board/Photo
This is a Polynomial in Factored Form (It looks similar to a Quadratic Function)
f(x) = 3(x-4)(x+3)2(x-7)2(x+8)2
What is the degree of this function
Hint: Just add all the exponents
7
(If you foiled out this function the highest power of f(x) would be 7, adding all the exponents gives you the same answer)
Vertical Lines always have a _______ Slope
Horizontal Lines always have a Slope of ______
Undefined
0
How many times was each game played? (Solve the system of equations)
The Carnival has a wheel spinning game and a dunk tank. The wheel costs $5 per game and the dunk tank costs $7 per game. The carnival made a total profit of $226. 40 games were played in total.
The Dunk Tank game was played 13 and the Wheel game was played 27 times
f(x) = 3x2+7
Find the average rate of change of f(x) on the interval [3,7]
30
Find the X-intercepts of the function
f(x) = 3(x+5)(x-4)
x = -5, 4
What are the X-Intercepts of this function?
f(x) = 3(x-4)(x+3)2(x-7)2(x+8)2
Bonus 100 Points
2) Does (x+3)2 bend or cut through the X-Axis
x= 4, -3, 7, -8
2) Bends because it has an even multiplicity
Finding the X-Intercepts or Zeros of a Polynomial is the same as finding the Zeros of a Quadratic.
Each (x-z1) is called a Factor
Multiplicity is the power that the Factor is raised to
Bob and Sally own a donut shop. They rent out out the building for $1500 a month. The cost of ingredients per dozen donuts is $13.
1) Write a function C(x) which represents the costs incurred by their donut shop?
2) If their monthly costs totaled $2150, how many dozen donuts did they make
Extra 200 Points
3) If their monthly cost totaled $2150 how many donuts did they make?
C(x)=13x+1500
50 Dozens
600 Donuts
Daily Double!!
John owns a snow shoveling company and Brad does too! John has $14 base fee and charges $5 per hour. Brad has a $30 base fee and charges $3 per hour.
1) At what numbers of hours are their Total Fees the same
2) Who is cheaper after the number of hours from part 1
3) Once we know the point where their totals fees are the same is their a way to see who will be cheaper without plugging in numbers
1) The totals fees are the same at 8 hours ($54)
2) After 8 hours Brad is cheaper
3) Once they are the same price Brad charges and rate, so from that point on he will be cheaper
Slide 2
2/3.9
Slide 4
Hint: Use f(x) = a(x-z1)(x-z2) to find the answer
f(x) = (3/121)(x+10)2
Slide 6
Bonus 200 Points
What are the 4 possible end behaviors?
-(x)Even
Board
Using Point-Slope Form find an equation that passes through the point (6,7) and (2,10)
Hint: y= m(x-x1)+y1
I'm looking for an equation that I can plug x values into
y= (-3/4)(x-2)+10
or
y= (-3/4)(x-6)+7
Come up with a scenario for a system of equations
Multiple correct equations
g(x) = 4x2+4
Find the average rate of change on the interval [3,3+h]
4h+24
Daily Double!!
(0,3)
(5,0)
(-4,0)
Assuming f(x) is a quadratic function, what is the function?
f(x)=(-3/20)(x+4)(x-5)
Slide 7
-(x)Odd