Question

name scott polkn date
reassess unit 6 sum 2 l8.11
complete the following questions without the use of graphing technology. show your work

1. select all expressions that are equivalent to $(x - 2)(2x - 4)$

$\square 2(x - 2)^2$
$\square 4(\frac{1}{2}x^2 - 2x + 2)$
$\square 2x^2 - 4$
$\square 2x^2 - 8x - 6$
$\square \frac{1}{2}(4x - 8)(x - 2)$
$\square 2x^2 - 8x + 8$

1. for each expression, write an equivalent expression in standard form. show all work. circle

your answers.
a. $(x - 2)(x + 7)$ b. $(3x + 5)(x - 3)$ c. $(x + 4)^2$

1. question 3 refers to the following graph:

a. which expression could define this function?
a) $(x + 3)(x - 1)$
b) $(x - 3)(1 - x)$
c) $(x + 1)(x - 3)$
d) $(x - 1)(3 - x)$
c. write the coordinates of the vertex. and plot the point
and label it with \v\.
d. write the coordinates of the y - intercept. and plot the point and label it \y - int\.

Explanation:

Step1: Expand \((x - 2)(2x - 4)\)

Use the distributive property (FOIL method):

$$
LATEXBLOCK0
$$

Step2: Expand \(2(x - 2)^{2}\)

First, \((x - 2)^{2}=x^{2}-4x + 4\). Then \(2(x^{2}-4x + 4)=2x^{2}-8x+8\)

Step3: Expand \(4(\frac{1}{2}x^{2}-2x + 2)\)

$$4\times\frac{1}{2}x^{2}-4\times2x+4\times2 = 2x^{2}-8x + 8$$

Step4: Expand \(\frac{1}{2}(4x - 8)(x - 2)\)

First, \(4x-8 = 4(x - 2)\). Then \(\frac{1}{2}\times4(x - 2)(x - 2)=2(x - 2)^{2}\). As shown in Step2, \(2(x - 2)^{2}=2x^{2}-8x + 8\)

Step5: Check \(2x^{2}-4\)

\(2x^{2}-4
eq2x^{2}-8x + 8\) (missing the linear - term and constant - term adjustment)

Step6: Check \(2x^{2}-8x-6\)

\(2x^{2}-8x-6
eq2x^{2}-8x + 8\) (constant - term is wrong)

Answer:

\(\boxed{2(x - 2)^{2}}\), \(\boxed{4(\frac{1}{2}x^{2}-2x + 2)}\), \(\boxed{\frac{1}{2}(4x - 8)(x - 2)}\), \(\boxed{2x^{2}-8x + 8}\)