9514 1404 393
Answer:
Vertex: (-1, 4)
Maximum: f(-1) = 4
Increasing: (-∞, -1)
Decreasing: (-1, ∞)
Step-by-step explanation:
The equation can be written in vertex form by "completing the square."
First factor out the leading coefficient from the x-terms.
f(x) = -(x² +2x) +3
Then add the square of half the x-coefficient inside parentheses. Add the opposite of that amount outside parentheses.
f(x) = -(x² +2x +1) +3 +1
Write in vertex form.
f(x) = -(x +1)² +4 . . . . . . . compare to a(x -h)² +k
You can see that the vertex is (h, k) = (-1, 4), and that the vertical scale factor 'a' is negative. This means the vertex is the maximum and the parabola opens downward.
The function will be increasing to the left of the maximum, decreasing to its right.
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Vertex: (-1, 4)
Maximum: f(-1) = 4
Increasing: (-∞, -1)
Decreasing: (-1, ∞)
Graph: see attached
If you round both numbers to the nearest thousand, you have 17,000 - 6,000 which is the best estimate.
Answer:
Step-by-step explanation:
Students are asked to write in the standard form.
Now, in the standard form of a polynomial the highest power of the variable takes the leftmost position and the lowest power of the variable takes the rightmost position and the power of variable decreases from left to right.
Therefore, the standard form will be . (Answer)
Answer:
≈ 452.5 rpm
Step-by-step explanation:
First convert mph to in/min.
35 mi/hr × (5280 ft/mi) × (12 in/ft) × (1 hr / 60 min) = 36960 in/min
The diameter of the wheel is 26 inches, so the circumference of the wheel is 26π inches. So the revolutions per minute is:
36960 in/min × (1 rev / 26π in) ≈ 452.5 rpm
Answer:
The correct answer is option (a) 001, 002, 003, . .. ,439, 440
Step-by-step explanation:
Sample size in the given statement is n = 10
Population size N = 440
So, we must label the population with numbers 001, 002, 003, . .. ,439, 440 so that each member of the population is correctly identified.