What is the midpoint of the x-intercepts of f(x) = (x – 4)(x + 4)?
2 answers:
Answer: The correct option is (A) (0, 0).
Step-by-step explanation: We are given to find the midpoint of the x-intercepts of the following quadratic function:
We know that the x-intercepts of a function f(x) is found by solving the equation f(x) = 0.
So, from equation (i), we have
That is, the x-intercepts of the given function are the points (4, 0) and (-4, 0).
Therefore, the co-ordinates of the mid-point of the x-intercepts (4, 0) and (-4, 0) will be
Thus, the required mid-point of the x-intercepts is (0, 0).
Option (A) is correct.
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We have been given that fuel efficiency for a 2007 passenger car was 31.2 mi/gal and the same model of car, the fuel efficiency increased to 35.6 mi/gal in 2012. Also, the gas tank for this car holds 16 gallons of gas.
We need to write a function and graph a linear function that models the distance that each car can travel for a given amount of gas up to one tankful.
Let represent the functions as and
where
and
represent the distances traveled by car in years 2007 and 2012 and x represents the number of gallons. Therefore, we can express the required functions as:
Domain of both these functions are [0,16] and ranges are [0,499.2] and [0,569.6] respectively for years 2007 and 2012.
The difference function will be:
Domain of this function is [0,16] and range is [0,67.2].
The graphs are shown below.
