###### 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 ...

a. Since $x^{3}-27=x^{3}-3^{3}$, we ...
Question: B.4.5

## Factoring the special products Factor each polynomial. a. 4x² – 1 b. x² – 6x + 9 c. 9y² + 30y + 25 ...

a.   4x² - 1 = (2x)² - 1²              Recognize t...
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. ...

We have $A=21, B=-10 \sqrt{3}$ ,  an...
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. ...

Since y = 1/x is equivalent to xy - 1 = 0, we have...
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? ...

Use the rotation equations  x^{\prime}=x \c...
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. ...

The graph that we seek is the graph of  \fr...
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. ...

Divide each side of the equation by 36 to get the ...
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). ...

The radius is the distance from (4, 5) to (-1, 2):...
Question: 10.2.4