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Butoxors [25]
3 years ago
12

describe the transformations that occur from the parent function f(x) =x^2 to the function g(x)=2(x+1)^2-7

Mathematics
1 answer:
irinina [24]3 years ago
5 0

translate 7 units down. One to the left. The quadratic function stretches vertically by a factor of 2.

Step-by-step explanation:

There are many factors that play transformations in quadratic functions.

Let me give you some rules to help you with transformations.

We know that the standard form for a quad function is y= ax^2+bx+c.

We can write that in vertex form.

The formula is y=a(x-h)^2+k.

a, h, and k can contribute to factors on the graph.

Let's start with a.

When a is greater than 1, the graph stretches vertically, or it is just a stretch.

If a is less than 1 but greater than 0, the graph shrinks or compresses.

A also determines if you have a maximum or minimum as well as if the graph opens up or down.

With h, that plays a role with the horizontal translation.

No specific rules here, but here, the reason why it is one unit to the left and not one unit to the right is because of the formula.

remember how it is x-h. On a graph, it would be -1.

So x--1 is x+1.

Don't get fooled by this.

Vice versa as well.

With vertical translation, however, you do not need to remember anything. If it says -7 it is translated 7 units down from the parent function or y=x^2.

I hope this helps!

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Bas_tet [7]
Given:

Current revenue = $6000

<span>R(f)= -100f^2 + 400f + 6000
where f is a whole number of $5 fee increases

We are told to find f, when R(f) </span><span>< 6000

Since </span>R(f)= -100f^2+400f+6000

R(f) < 6000 ⇒ -100f^2+400f+6000 < 6000


Subtract 6000 from both sides

-100f^2 + 400f + 6000 - 6000 < 6000 - 6000

-100f^2 + 400f < 0

⇒ 400f - 100f^2 < 0


Divide the equation by 100

400f/100 - 100f^2/100 < 0/100

4f - f^2 < 0


Add f^2 to both sides of the equation

4f - f^2 + f^2 < 0 + f^2

4f < f^2


Divide both sides by f

4f/f < (f^2)/f

4 < f

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8 0
3 years ago
City planners are creating a 3-dimenslonal model of a city park to find the best placement for a new tennis court the city park
xxTIMURxx [149]

The dimension of the tennis court in the scaled model is 0.6 ft long and 0.3 ft wide.

Given, a rectangular plot of land that is 1,500 ft long and 600 ft wide the scale model of the park measures 7.5 ft x 3 ft.

The actual tennis court must be 120 ft long and 60 ft wide, then we need to find the dimensions of the tennis court in the scale model.

<h3>What is a scaled model?</h3>

A scale model is a physical model which is geometrically similar to an object. Scale models are generally smaller than large prototypes such as vehicles, buildings, or people.

First, divide the original measurements by the scaled ones. We get

1500 ft. ÷7.5 ft = 200

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Now, divide tennis courts actual dimensions by 200. That is

120 ft. ÷ 200 = 0.6 ft

60 ft. ÷ 200 =  0.3 ft

Therefore, the dimension of the tennis court in the scaled model is 0.6 ft long and 0.3 ft wide.

To learn more about scale factor visit:

brainly.com/question/22312172.

#SPJ1

5 0
2 years ago
Passed with 100%
alex41 [277]
I would answer this but I am not sure
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astraxan [27]

Answer:

Why not

Step-by-step explanation:

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saw5 [17]

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