Lesson 6 Stretching My Quads Practice Understanding

Ready

Solve for $x$ .

1.

$x + 23 = 0$

2.

$x - 11 = 0$

3.

$5 x - 35 = 0$

4.

$9 x + 63 = 0$

5.

$4 x - 3 = 0$

6.

$6 x + 17 = 0$

7.

$\frac{2}{3} x + 18 = 8$

8.

$\frac{6}{7} x + 2 = 8$

9.

$\frac{5}{9} x - 23 = 7$

Set

Use technology to graph each function. Use the graph to find the vertex, the line of symmetry, the $y$ -intercept, and the $x$ -intercepts. Be sure to properly write the intercepts as points.

10.

$y = (x + 1) (x - 3)$

Line of symmetry:

Vertex:

$x$ -intercepts:

$y$ -intercept:

If $(x + 1) (x - 3) = 0$ , what are the solutions to the equation?

11.

$y = 2 (x + 1) (x - 3)$

Line of symmetry:

Vertex:

$x$ -intercepts:

$y$ -intercept:

If $2 (x + 1) (x - 3) = 0$ , what are the solutions to the equation?

12.

Compare the graph in #11 with the graph in #10.

a.

Identify the features that stayed the same.

b.

Which features changed value?

13.

$y = (x - 2) (x + 8)$

Line of symmetry:

Vertex:

$x$ -intercepts:

$y$ -intercept:

If $(x - 2) (x + 8) = 0$ , what are the solutions to the equation?

14.

$y = - 3 (x - 2) (x + 8)$

Line of symmetry:

Vertex:

$x$ -intercepts:

$y$ -intercept:

If $- 3 (x - 2) (x + 8) = 0$ , what are the solutions to the equation?

15.

Compare the graph in #14 with the graph in #13.

a.

Identify the features that stay the same.

b.

Which features changed value?

16.

Explain the role of the stretch factor in the equation of a quadratic. Include what features it affects and how it affects the graph.

Go

Rewrite each expression without negative exponents or common factors.

17.

$4^{- 3} w^{5} x^{- 3} y^{- 9} z^{4}$

18.

${(8^{- 2} a^{- 3} b^{- 1} c^{- 6} d^{10})}^{- 1}$

19.

$\frac{r^{8} s^{- 5} t^{- 2} t^{6}}{7^{- 2} s^{9} t^{7}}$

20.

$\frac{5^{- 2} a^{- 3} b^{4} c^{10} d^{6}}{5 b^{- 2} c^{- 3} d^{9} e}$

21.

$\frac{3 a^{11} s^{- 5} d^{- 2} f^{8}}{3^{- 3} a^{7} s^{- 5} d^{13} f^{6}}$

22.

$w^{- 9} e^{2} e^{- 7} r^{- 16} r^{10}$

23.

$8 {(x^{3})}^{- 7} y^{5}$

24.

${(\frac{4 a b^{2}}{5})}^{- 2} \cdot {(\frac{4 a b^{2}}{5})}^{2}$

25.

${(\frac{9 a^{7} b^{4} c^{- 1}}{10})}^{- 2} \cdot {(\frac{50 c^{2}}{72 b^{8}})}^{- 1}$