Choose the expression which represents the simplest form of (-4x2)

WINSTONCH [101]

The graph of y = 2(x - 3)² + 2 can be seen in the attached picture. This problem can be solved through the concept of parabola and transformation.

<h3>Further explanation</h3>

<u>The Problem:</u>

Which is the graph of y = 2(x - 3)² + 2?

<u>Question-1:</u>

How to make a graph y = 2 (x - 3) ² + 2 through the concept of a parabola.

<u>The Process:</u>

The equation of a parabola is given by $\boxed{ \ y = a(x - h)^2 + k \ }$ .

Keep in mind the following points:

vertex point at (h, k)
axis of symmetry at x = h
a > 0 the parabola opens upward
a < 0 the parabola opens downward
the y-intercept is $\boxed{ \ y = ah^2 + k \ }$ at x = 0.

From our case it can be concluded as follows:

the graph of y = 2(x - 3)² + 2 opens upward
vertex point at (3, 2)
axis of symmetry at x = 3
the y-intercept is 2(3²) + 2 = 20 or in coordinates of (0, 20)

<u>Question-2:</u>

How to make the graph of y = 2(x - 3)² + 2 through the transformation.

<u>The Process:</u>

To plot the graph of y = 2(x - 3) ² + 2 we apply for the following transformation order:

Step-1: clearly, to obtain the graph of y = (x - 3)² we shift the graph of y = x² to the right 3 units.

Step-2: to obtain the graph of y = 2(x - 3)², we stretch the graph of y = (x - 3)² by a factor of 2 (in other words, multiply each y-coordinate by 2).

Step-3: finally, to obtain the graph of y = 2(x - 3)² + 2 we shift the graph of y = 2(x - 3)² upward 3 units.

Thus the construction of the graph y = 2 (x - 3) ² + 2 is completed.

The graph of y = 2(x - 3) ² + 2 is drawn by the combination of shifting the graph of y = x² to the right 3 units and upward 2 units, and also stretch by a factor of 2. Between vertical shift and stretch steps, it is the same whatever steps are taken first.

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Notes

The transformation of graphs is changing the shape and location of a graph.
There are four types of transformation geometry: translation (or shifting), reflection, rotation, and dilation (or stretching/shrinking).
In this case, the transformation is shifting horizontally and vertically and also stretching vertically.

In general, given the graph of y = f(x) and v > 0, we obtain the graph of:

$\boxed{ \ y = f(x) + v \ }$ by shifting the graph of $\boxed{ \ y = f(x) \ }$ upward v units.
$\boxed{ \ y = f(x) - v \ }$ by shifting the graph of $\boxed{ \ y = f(x) \ }$ downward v units.

That's the vertical shift, now the horizontal one. Given the graph of y = f(x) and h > 0, we obtain the graph of:

$\boxed{ \ y = f(x + h) \ }$ by shifting the graph of $\boxed{ \ y = f(x) \ }$ to the left h units.
$\boxed{ \ y = f(x - h) \ }$ by shifting the graph of $\boxed{ \ y = f(x) \ }$ to the right h units.

Hence, the combination of vertical and horizontal shifts is as follows:

$\boxed{ \ y = f(x \pm h) \pm v \ }$

The plus or minus sign follows the direction of the shift, i.e., up-down or left-right .

Notice the following definitions for stretch and shrink.

In general, given the graph of $\boxed{y = f(x)}$ , we obtain the graph of $\boxed{y = cf(x)}$ by stretching $\boxed{ \ c > 1 \ }$ or shrinking $\boxed{ \ 0 < c < 1 \ }$ the graph of $\boxed{y = f(x)}$ vertically by a factor of c.
In general, given the graph of $\boxed{y = f(x)}$ , we obtain the graph of $\boxed{y = f(cx)}$ by stretching $\boxed{ \ 0 < c < 1 \ }$ or shrinking $\boxed{ \ c > 1 \ }$ the graph of $\boxed{y = f(x)}$ horizontally by a factor of c.

<h3>Learn more </h3>

What is the y-intercept of the quadratic function f(x) = (x – 6)(x – 2)? brainly.com/question/1332667
Transformations that change the graph of (f)x to the graph of g(x) brainly.com/question/2415963
Which statement correctly describes the graph brainly.com/question/10929552

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100times bigger than 2

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Answer:

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A teacher decides to purchase a new car and considers two options. Option one is the new Zoomba for $60,000 with an expected dep

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The teacher chose option 2, the Starfish and it was valued at $35,200 after two months.

Step-by-step explanation:

Step 1; The Zoomba is priced at $60,000 and has an expected depreciation of 2% per month. So the annual depreciation is 12 months * 2% per month = 24% per year. The teacher plans to keep either car for two years do total depreciation is 2 years * 24% depreciation per year = 48 % in two years.

Value of car after two years = Buying price - Depreciation amount

= $60,000 - 48% of $60,000 = $60,000 - 0.48*$60,000 = $31,200

The car will be valued at $31,200 after two years. To determine how much value it has retained we divide the value in two years to the current value i.e $31,200 divided by $60,000 which equals 0.52 (52% of initial price)

Step 2; The Starfish is priced at $40,00 and will depreciate $200 every month. For a year it will depreciate 12 months * $200 per month = $2,400 a year. So for a total of two years a depreciaition of $4,800.

Value of car after two years = Buying price - Depreciation amount

= $40,000 - $4,800 = $35,200

The car will be valued at $35,200 after two years. To see the retained value we divide the depreciated value by the current value i.e. $35,200 divided by $40,000 which equals 0.88 (88% of the initial price)

Step 3; Of the two options, the Starfish retains more of its value over two years. So the teacher chose the Starfish over the Zoomba.

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