WorksheetsUnit 3 - Review - REAL Quadratics
Total questions: 13
Worksheet time: 7mins
A company selling school supply kits determines that its revenue can be modeled by the function 𝑓(𝑥) = 9.5𝑥 − 0.05𝑥2, where 𝑥 represents the number of kits sold per day and 𝑓(𝑥) represents the daily revenue.
WHAT ARE THE PROPER CONSTRAINTS ON the problem? Think about the x-values!
[0,95)
x cannot be greater than 0 or less than 190
Domain is (0,190)
(95,451.25)
A company selling school supply kits determines that its revenue can be modeled by the function 𝑓(𝑥) = 9.5𝑥 − 0.05𝑥2, where 𝑥 represents the number of kits sold per day and 𝑓(𝑥) represents the daily revenue.
IDENTIFY the VERTEX of the problem
(0,0)
(451.25,190)
(190,0)
(95,451.25)
A company selling school supply kits determines that its revenue can be modeled by the function 𝑓(𝑥) = 9.5𝑥 − 0.05𝑥2, where 𝑥 represents the number of kits sold per day and 𝑓(𝑥) represents the daily revenue.
IDENTIFY the x-intercepts of the problem
(0,0) and (190,0)
(451.25,190) and(0,0)
(190,0) and (95,451.25)
(95,451.25) and (0,0)
A company selling school supply kits determines that its revenue can be modeled by the function 𝑓(𝑥) = 9.5𝑥 − 0.05𝑥2, where 𝑥 represents the number of kits sold per day and 𝑓(𝑥) represents the daily revenue.
WHAT DO THE x-intercepts represent?
They represent the number of days it will take to reach a revenue of 0 or 190.
They represent the revenue of $0. This occurs when the # of kits sold per day are 0 and 190
They represent the # of school supply kits when the revenue is at the vertex
They represent the amount of items inside a supply kit which would bring the revenue to 0.
A company selling school supply kits determines that its revenue can be modeled by the function 𝑓(𝑥) = 9.5𝑥 − 0.05𝑥2, where 𝑥 represents the number of kits sold per day and 𝑓(𝑥) represents the daily revenue.
Use the GRAPH to approximate the solutions to 250 = 9.5𝑥 − 0.05𝑥2
x = 0 and x = 190
x = 0 and x = 250
x = 15, x = 310
x = 30 and x = 160
A company selling school supply kits determines that its revenue can be modeled by the function 250 = 9.5𝑥 − 0.05𝑥2, where 𝑥 represents the number of kits sold per day and 𝑓(𝑥) represents the daily revenue.
What do the x-intercepts mean in the context of this problem?
The revenue will never be $250 because it is impossible to sell more than 29 kits per day.
When the # of kits sold per day is around 30 or 160, the revenue will be $250
The revenue will be $30 or $160 when the number of kits sold per day is 250
The Revenue will be $160-30 = $130 per day
A company selling school supply kits determines that its revenue can be modeled by the function 𝑓(𝑥) = 9.5𝑥 − 0.05𝑥2, where 𝑥 represents the number of kits sold per day and 𝑓(𝑥) represents the daily revenue.
Where on the function is the INTERVAL INCREASING? (Write in Interval Notation)
(0,95)
(0,190)
[0,95]
(-30,95]
A company selling school supply kits determines that its revenue can be modeled by the function 𝑓(𝑥) = 9.5𝑥 − 0.05𝑥2, where 𝑥 represents the number of kits sold per day and 𝑓(𝑥) represents the daily revenue.
Where on the function is the INTERVAL DECREASING? (Write in Interval Notation)
(0,95)
(0,190)
[95,190]
(95,190)
What is the difference between FACTORING and SOLVING and equation?
You cannot do one without the other. You MUST factor to find a solution.
Factoring means finding all the factors of an expression, Solving means find x. There are many ways to solve for x.
They are the same.
Factoring means find what multiplies to c and adds to b, solving means look for y.
How can you solve this equation?
y = 2x2+7x-30
Use the quadratic formula
Factor and solve for x.
Complete the Square to solve for x.
All of the above.
SOLVE.
y = 2x2+7x-30
x = -6, x = 5/2
x =6, x = -5/2
Complete the Square to solve for x.
x = 6i and -5/2
How would you find the solutions of this problem, which is already factored?
x2(x-5)(2x-1) = 0
plug zero into every x value.
multiply using the distributive method
Set each factor to 0 and solve for x.
walk away!
The following is in factored form. What are all the solutions?
x2(x-5)(2x-1) = 0
x = 1, 1, -5, and 1/2
x = 1/2,-5, 1
x = 5,1/2
x = 0, 5, 1/2
