The quadratic functions f(x) and g(x) are described as follows: f(x) = −4x2 + 5 x g(x) 0 0 1 1 2 5 3 1 4 0 Which of the followin
g statements best compares the maximum value of the 2 functions?
It is the same for both functions.
f(x) has a greater maximum value than g(x).
g(x) has a greater maximum value than f(x).
The maximum values cannot be determined.
It is the same for both functions.
f(x) has a greater maximum value than g(x).
g(x) has a greater maximum value than f(x).
The maximum values cannot be determined.
1 answer:
The equation describes a function whose maximum value is 5. The data set describes a function whose maximum value is also 5. Comparing the maximum values, we must conclude ...
... It is the same for both functions.
_____
Please note that the premise is that g(x) is a quadratic function. It is definitely NOT a quadratic function in the usual sense of the term.
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In order to divide integers, the first thing to check is the sign:
- When dividing two positive integers, the result will be a positive integer.
- When dividing two negative integers, the result will be a positive integer.
- When dividing integers with different signs (one negative and one positive), the result will be a negative integer.
Then, after checking the sign, we need to calculate the value of the division.
Some examples of divisions are:
In the first division, the result is 3, because we have that 8 * 3 is equal 24.
Also, both numbers are positive, so the result is also a positive number.
In the second division, the result is -3, because 5 * (-3) is equal -15.
The result is negative, because the two numbers have different signs.
In the third division, the result is 10, because -10 * 10 is equal -100.
The result is positive, because both numbers are negative.
Notice that
13 - 9 = 4
17 - 13 = 4
so it's likely that each pair of consecutive terms in the sum differ by 4. This means the last term, 149, is equal to 9 plus some multiple of 4 :
149 = 9 + 4k
140 = 4k
k = 140/4
k = 35
This tells you there are 35 + 1 = 36 terms in the sum (since the first term is 9 plus 0 times 4, and the last term is 9 plus 35 times 4). Among the given options, only the first choice contains the same amount of terms.
Put another way, we have
but if we make the sum start at k = 1, we need to replace every instance of k with k - 1, and accordingly adjust the upper limit in the sum.