Lesson 2 Getting Centered Solidify Understanding

Ready

Figure 1 shows the graph of the function $f (x) = \sqrt[3]{x}$ .

Write the equation for each transformation of $f (x) = \sqrt[3]{x}$ .

1.

$f (x) = \sqrt[3]{x}$ is moved to the left $6 units$ and up $3 units$ . It also undergoes a vertical stretch by a factor of $\frac{1}{2}$ .

2.

$f (x) = \sqrt[3]{x}$ is moved to the left $11 units$ and up $8 units$ . It also undergoes a vertical stretch by a factor of $4$ .

For problems 3 and 4, use the graph to write the equation of the transformed function.

3.

$f (x)$ looks like Figure 2.

4.

$f (x)$ looks like Figure 3.

Set

5.

Write the equation of a circle congruent to $⨀ C$ with center at point $P$ .

6.

Write the equation of a circle centered at $T (- 7, - 3)$ and with a radius equal to the hypotenuse of $△ A B C$ .

7.

Write the equation of $⨀ V$ .

Write the equation of the circle with the given center and radius.

Then write it in general form: $x^{2} + y^{2} + A x + B y + C = 0$ .

8.

Center: $(5, 2)$ Radius: $13$

9.

Center: $(- 6, - 10)$ Radius: $9$

10.

Center: $(0, 8)$ Radius: $15$

11.

Center: $(19, - 13)$ Radius: $1$

12.

Center: $(- 1, 2)$ Radius: $10$

13.

Center: $(- 3, - 4)$ Radius: $8$

Go

Solve for $x$ .

14.

$47 = \frac{4}{3} x + 15$

15.

$2 x - 13 = 6 x + 15$

16.

$3 x + 18 = 2 \frac{1}{2} x + 40$

17.

$x^{2} + 17 x = 38$

18.

$- 180 = - 4 x^{2} + 720$

19.

$x^{2} - 120 = 1$

20.

$4 x^{2} + 52 x + 169 = 0$