The graph below shows the number of visitors at a theme park. How many more visitors in total went to the park in June, July and
August in Year 2 than Year 1?
1 answer:
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Answer:
Calculate the <u>first differences</u> between the y-values:
As the first differences are <u>not the same</u>, we need to calculate the <u>second differences</u>:
As the second differences are the <u>same</u>, the relationship between the variable is quadratic and will contain an term.
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<u>To determine the quadratic equation</u>
The coefficient of is always <u>half</u> of the <u>second difference</u>.
As the second difference is 2, and half of 2 is 1, the coefficient of is 1.
The standard form of a quadratic equation is:
(where a, b and c are constants to be found).
We have already determined that the coefficient of is 1.
Therefore, a = 1
From the given table, when ,
.
Finally, to find b, substitute the found values of a and c into the equation, then substitute one of the ordered pairs from the given table:
Therefore, the quadratic equation for the given ordered pairs is:
