Answer:
Part 1) Option B: 0 ≤ x ≤ 4
Part 2) Option C: (5x − 1)(2x − 3)
Part 3) Option C: The crop yield decreased by 10 pounds per acre from year 10 to year 20.
Part 4) Option B: f(x) = (2x + 1)(2x − 1)
Part 5) Option A: The company earned 85 billion dollars in 2008
Part 6) Option C: (3, 0) and (5, 0)
Step-by-step explanation:
Part 1) we have
This is a vertical parabola open downward
The vertex is a maximum
The x-intercepts are the points (0,0) and (4,0)
The vertex is the point (2,20) ---> The x-coordinate of the vertex is the midpoint of the x-intercepts
so
The domain is the interval ----> [0,4]
The range is the interval ----> [0,20]
Part 2) we have
where
x is the time in minutes
V is the volume in gallons
we know that
When the trough is empty, the volume is equal to zero
so
For V=0
The formula to solve a quadratic equation of the form
is equal to
in this problem we have
so
substitute in the formula
so
simplify
Part 3) we have
we know that
To find the average rate of change, we divide the change in the output value by the change in the input value
the average rate of change is equal to
In this problem we have
Substitute
----> is a decreasing function
therefore
The crop yield decreased by 10 pounds per acre from year 10 to year 20.
Part 4) we have
<em>Find out the x-intercepts</em>
Remember that the x-intercepts are the values of x when the value of the function is equal to zero
so
For f(x)=0
Solve for x
take square root both sides
so
Part 5) we have
Remember that
The y-intercept of a function is the value of the function (output value) when the value of x (input value) is equal to zero
In this problem
The expression represent a company's net sales, in billions, from 2008 to 2018
t is the number of years since the end of 2008
so
For t=0 -----> represent the end of 2008
therefore
The company earned 85 billion dollars in 2008.
Part 6) What are the x-intercepts of the parabola?
we have the points (2,3),(4,-1),(6,3)
This is a vertical parabola open upward
The vertex represent a minimum
In this problem the vertex is the point (4,-1)
The equation of a vertical parabola in vertex form is equal to
where
a is a coefficient
(h,k) is the vertex
we have
(h,k)=(4,-1)
substitute
take the point (2,3) and substitute in the quadratic equation to solve for a
For x=2, y=3
The quadratic equation is
Find out the x-intercepts
Remember that the x-intercepts are the values of x when the value of the function is equal to zero
so
For y=0
Solve for x
take square root both sides
therefore
The x-intercepts are the points (3,0) and (5,0)