The rate of change of positive at the increasing interval and it is negative at the decreasing interval
The equation of the parabola
The graph has two x-intercepts at x = 1.5 and x = 8.
So, the equation can be represented as:
y = a(x - 1.5)(x - 8)
The graph passes through the point (0, -1.2).
So, we have:
a(0 - 1.5)(0 - 8) = -1.2
Solve for a
a= -0.1
Substitute a= -0.1 in y = a(x - 1.5)(x - 8)
y = -0.1(x - 1.5)(x - 8)
Hence, the equation of the parabola is y = -0.1(x - 1.5)(x - 8)
The highest slide
This is the maximum value of the graph.
The graph has its maximum at (4.75,1.056)
Hence, the highest slide is 1.056
The average rate of change when the tide is increasing
From the given graph, the tide increases from (0,-1.2) to (4.75,1.056)
The average rate of change is;
[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{1.056 + 1.2}{4.75 -0}[/tex]
Evaluate
m = 0.475
Hence, the average rate of change when the tide is increasing is 0.475
The average rate of change when the tide is decreasing
From the given graph, the tide increases from (4.75,1.056) to (8,0)
The average rate of change is;
[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{1.056 -0}{4.75 -8}[/tex]
Evaluate
m = -0.325
Hence, the average rate of change when the tide is decreasing is -0.325
Conclusion about the rates of change
When the tide increases, the rate of change of positive (i.e. 0.475) and it is negative when the tide is decreasing
Read more about rates of change at:
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