Alg 2:1 CAN #9 -Performance Task: Trigonometric Relationships: Owls and Mice M4 Topics 1 and 2: Trigonometric Relationshlps and Trigonometric Equations A scientist is researching the various types of prey hunted by barn owls in one area of his state. He discovered that the main prey hunted by the barn owl is a field mouse. The scientist studied the population of field mice and realized that the population could be modeled by the function M(t) = 250 sin ( t +)+ 580, Need Help? Refer to Week 30e Lesson 1.4 where t is time in months since the study began, and M(t) is the mice population. Recall the transformations for the sine function can be written in the the form: Transformation of Sine and Cosine Functions y= Asin(Bx - C) + D A = Amplitude = Period b| = Phase Shift (left or right) D = Vertical Shift and y = Dis the midline Step 1: Graph the function for 0s ts 20 2. Identify each of the following characteristics of the equation and graph, and explain how it relates to the context of the problem. a. What is the vertical translation and equation of the midline? What does it mean in context?(Hint: think average) The average amount of b. What is the Amplitude? What does it mean in context?(Hint: think variation and population)

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Q: + + + -5 -2+ -4

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A: We have to find function rule

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A: see below the graph of the equation given in the question

Q: Does the graph represent y as a function of x

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Q: Determine which graph represent a constant function. A B D

A: Let's find.

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Q: 2. Compare the functions in the following graph: 10 y=-x^2+4 y=-2x+1 - 10 2.

A: y=-x2+4 and y=-2x+1

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Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.