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AysviL [449]
3 years ago
8

Vertex Form of Quadratic Functions

Mathematics
1 answer:
Nikitich [7]3 years ago
8 0
The X-intercepts: (1,0),(-7,0)

Axis of symmetry: x= - 3

The vertex: (-3, -8)

The Y-intercept: (0, -7/2)

Concave up or down: concave up

Sketch: a poorly drawn picture on the bottom.

I hope that helps.

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f(x)=x^2; vertical shrink by a factor of 1/2 and a reflection in the y-axis, followed by a translation 1 unit down​
NeX [460]

The image of the function f(x) after vertical shrink by a factor of 1/2

and a reflection in the y-axis, followed by a translation 1 unit down​

is g(x) = \frac{1}{2} x² - 1

Step-by-step explanation:

Lets revise:

1. The vertical shrink

A vertical shrinking is the squeezing of the graph toward the x-axis.

if 0 < k < 1 (a fraction), the graph of y = k•f(x) is the graph of f(x) vertically

shrunk by multiplying each of its y-coordinates by k

2. The reflection

If the function f(x) reflected across the y-axis, then its image is g(x) = f(-x)

3. Vertical translation

If the function f(x) translated vertically up  by m units, then its image

is g(x) = f(x) + m

If the function f(x) translated vertically down  by m units, then its image

is g(x) = f(x) - m

Now let us solve the problem

∵ f(x) = x²

∵ f(x) shrunk by a factor of \frac{1}{2}

∴ The image of f(x) = \frac{1}{2} x²

∵ The image of f(x) reflected across y-axis

∴ The sign of x will change

∴ The new image of f(x) = \frac{1}{2} (-x)²

∵ The new image of f(x) translated 1 unit down

∴ We will subtract the new image of f(x) by 1

∴ The last image of f(x) is g(x) = \frac{1}{2} (-x)² - 1

<em>V.I.Note:</em>

(-x)² = x² because even exponents reject the negative sign

The image of the function f(x) after vertical shrink by a factor of 1/2

and a reflection in the y-axis, followed by a translation 1 unit down​

is g(x) = \frac{1}{2} x² - 1

The attached graph for more understand

Learn more:

you can learn more about transformation in brainly.com/question/2415963

#LearnwithBrainly

4 0
3 years ago
You roll 2 dice and flip a coin. What's the probability of getting two 4's and a tails?
zubka84 [21]

Answer:

2/4

Step-by-step explanation:

7 0
3 years ago
What is 2+2 then take away 1
laiz [17]

Answer:

3

Step-by-step explanation:

2 + 2 = 4

4 - 1 = 3

4 0
3 years ago
Read 2 more answers
Find the 12th term of following geometric sequence 5, 20,80, 320,
vesna_86 [32]
5, 20, 80, 320, 1280, 5120, 20480, 81920, 327680, 1310720, 5242880, 20971520

The 12th term would be 20,971,520
Everything is being multiplied by 4 each time
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3 years ago
There are 16 competitors in the MATHCOUNTS Trainer competition, including 3 from Vienna. The gold medal goes to first place, sil
Brums [2.3K]

Answer:

1404

Step-by-step explanation:

13*12*9

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