Write an equation of a parabola that passes through the point (2,4) with vertex (-1,-1) in vertex form.
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Answer:
<em>The table shows an exponential function</em>
Step-by-step explanation:
<u>Linear vs Exponential Functions</u>
A linear function is written as:
where m and b are constants.
If a table contains a linear function, then for each pair of ordered pairs (x1,y1) and (x2,y2), the value of m must be constant.
The slope can be calculated as:
An exponential function is written as:
Where r is the ratio and yo is a constant.
If a table contains an exponential function, for two ordered pairs (x1,y1) and (x2,y2), the value of r must be constant.
The ratio can be calculated as:
Calculate the slope for (0,4) and (1,2):
Calculate the slope for (1,2) and (2,1):
Since the slope is not the same, the function is not linear.
Now calculate the ratio for (0,4) and (1,2)
The radical of index 1 is simply equal to its argument:
Now calculate the ratio for (0,4) and (2,1)
Testing other points we'll find the same ratio, thus the table is an exponential function