Write the next three terms of the arithmetic sequence.
2 answers:
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Answer:
<em>Maximum: (-1,9)</em>
Step-by-step explanation:
<u>Vertex form of the quadratic function</u>
If the graph of the quadratic function has a vertex at the point (h,k), then the function can be written as:
Where a is the leading coefficient.
We are given the following function:
To find the vertex, we need to complete squares. First, factor -2 on the first two terms:
The expression in parentheses must be completed to represent the square of a binomial. Adding 1 and subtracting 1:
Taking out the -1:
Factoring the trinomial and operating:
Comparing with the vertex form we have
Vertex (-1,9)
Leading coefficient: -2
Since the leading coefficient is negative, the function has a maximum value at its vertex, i.e.
Maximum: (-1,9)
Answer:
y = 28
Step-by-step explanation:
Given that y varies directly as x and inversely as z then the equation relating them is
y = ← k is the constant of variation
To find k use the condition y = 4 when x = 2 and z = 7, then
4 = ( multiply both sides by 7 )
28 = 2k ( divide both sides by 2 )
14 = k
y = ← equation of variation
When x = 6 and z = 3 , then
y = = 14 × 2 = 28