a test battery contains the following three items: distance runs, skinfolds, and trunk extension. what does that test battery me
1 answer:
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Answer:
Part 1) (the missing steps in the explanation)
Part 3) (8, 4); The vertex represents the maximum profit
Part 4) x = 3.58, 0.42
Part 5) x = 6, x = 44; The zeros represent the number of monthly memberships where no profit is made
Part 6) 2(x − 7)2 + 118; x = $7
Part 7) The maximum height of the puck is 4 feet. −(x − 4)^2 + 6
Part 8) (x + 3)^2 − 4
Part 9) 2(x − 1)^2 = 4
Part 10) 8(x − 4)^2 + 592
Step-by-step explanation:
Part 1) we have
Convert to vertex form
step 1
Factor the leading coefficient and complete the square
step 2
step 3
Rewrite as perfect squares
Part 3) we have
we know that
This is the equation of a vertical parabola open downward
The vertex is a maximum
Convert to vertex form
Factor the leading coefficient
Complete the squares
Rewrite as perfect squares
The vertex is the point (8,4)
The vertex represent the maximum profit
Part 4) Solve for x
we have
square root both sides
Part 5) we have
we know that
The zeros or x-intercepts are the value of x when the value of the function is equal to zero
so
In this context the zeros represent the number of monthly memberships where no profit is made
To find the zeros equate the function to zero
Factor -1 of the leading coefficient
Complete the squares
Rewrite as perfect squares
square root both sides
Part 6) we have
This is a vertical parabola open downward
The vertex is a maximum
Convert the equation into vertex form
Factor the leading coefficient
Complete the square
Rewrite as perfect square
The vertex is the point (7,118)
therefore
The video game price that produces the highest weekly profit is x=$7
Part 7) we have
Convert to vertex form
Factor -1 the leading coefficient
Complete the square
Rewrite as perfect square
The vertex is the point (4,6)
therefore
The maximum height of the puck is 4 feet.
Part 8) we have
Convert to vertex form
Group terms
Complete the square
Rewrite as perfect squares
Part 9) we have
This is the equation of a vertical parabola open upward
The vertex is a minimum
Convert to vertex form
Factor 2 the leading coefficient
Complete the square
Rewrite as perfect squares
The vertex is the point (1,-4)
Part 10) we have
This is the equation of a vertical parabola open upward
The vertex is a minimum
Convert to vertex form
Factor 8 the leading coefficient
Complete the square
Rewrite as perfect squares
the vertex is the point (4,592)
The population has a minimum at x=4 years ( that is after 4 years since 1998 )
Answer:
vertex = (2, - 9 )
Step-by-step explanation:
Given a quadratic in standard form : ax² + bx + c : a ≠ 0
Then the x- coordinate of the vertex is
= -
x² - 4x - 5 ← is in standard form
with a = 1, b = - 4, thus
= -
= 2
Substitute this value into the quadratic for corresponding value of y
(2)² - 4(2) - 5 = 4 - 8 - 5 = - 9
vertex = (2, - 9 )