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Precalculus Functions and Graphs
535 SOLVED PROBLEMS
Question: B.4.6
Factoring differences and sums of two cubes Factor each polynomial. a. x³ – 27 b. 8w^6 + 125z³ ...
Question: B.4.5
Factoring the special products Factor each polynomial. a. 4x² – 1 b. x² – 6x + 9 c. 9y² + 30y + 25 ...
Question: 10.4.6
Rotation of axes for an ellipse Use rotation of axes to write 21x² – 10√3xy + 31y² = 144 in the standard form of an ellipse and sketch its graph. ...
Question: 10.4.5
Rotation of axes for a hyperbola Use rotation of axes to write y = 1/x in the standard form for a hyperbola. ...
Question: 10.4.3
Relating the coordinates Suppose that the x- and y-axes are rotated through the angle π/3. If the point P has coordinates (2, 5) in the xy-system, then what are the coordinates of P in the x’y’-system? ...
Question: 10.3.3
Graphing a hyperbola centered at (h, k) Determine the foci and equations of the asymptotes, and sketch the graph of (x – 2)²/9 – (y + 1)²/4 = 1. ...
Question: 10.3.2
Graphing a hyperbola opening up and down Determine the foci and the equations of the asymptotes, and sketch the graph of 4y² – 9x² = 36. ...
Question: 10.2.5
Finding the equation for a circle Write the equation for the circle that has center (4, 5) and passes through (-1, 2). ...
Question: 10.2.4
Graphing an ellipse centered at (h, k) Sketch the graph and identify the foci of the ellipse (x – 3)²/25 + (y + 1)²/9 = 1. ...
Question: 10.2.2
Graphing an ellipse with foci on the x-axis Sketch the graph and identify the foci of the ellipse x²/9 + y²/4 = 1. ...
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