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omeli [17]
3 years ago
13

How is the graph of the parent quadratic function transformed to produce the graph of y = negative (2 x + 6) squared + 3?

Mathematics
2 answers:
bearhunter [10]3 years ago
5 0

We start with the parent function

f(x)=x^2

The first child function would be

g(x)=(2x)^2

We have multiplied the input of the function by a constant: we have

g(x)=f(2x)

This kind of transformation result in a horizontal stretch/compression. If the multiplier is greater than 1, we have a compression. So, this first child causes a horizontal compression with compression rate 2.

The second child function would be

h(x)=(2x+6)^2

We added 6 to  the input of the function: we have

h(x)=g(x+6)

This kind of transformation result in a horizontal translation. If the constant added is positive, we translate to the left. So, this second child causes a translation 6 units to the left.

The third child function would be

l(x)=-(2x+6)^2

We changed the sign of the previous function (i.e. we multiplied it by -1): we have

l(x)=-h(x)

This kind of transformation result in a vertical stretch/compression. If the multiplier is greater than 1 we have a stretch, if it's between 0 and 1 we have compression. If it's negative, we reflect across the x axis, and then apply the stretch/compression. In this case, the multiplier is -1, so we only reflect across the x axis.

The fourth child function would be

m(x)=-(2x+6)^2+3

We added 3 to previous function: we have

m(x)=l(x)+3

This kind of transformation result in a vertical translation. If the constant added is positive, we translate upwards. So, this last child causes a translation 3 units up.

Recap

Starting from the parent function y=x^2, we have to:

  • Compress the graph horizontall, with scale factor 2;
  • Translate the graph 6 units to the left;
  • Reflect the graph across the x axis;
  • Translate the graph 3 units up

Note that the order is important!

blsea [12.9K]3 years ago
5 0

Answer:

B

Step-by-step explanation:

i know the other answer was a little confusing, but they did more, so feel free to give them brainliest, just wanted to help clarify :)

edgenuity 2020

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A store has clearance items that have been marked down by 25%. They are having a sale, advertising an additional 40% off clearan
Hatshy [7]

Answer: He would pay 45% of the original price.

Step-by-step explanation:

Since we have given that

Let the original price of item be 'x'

Rate mark down by 25%

Amount of marked down would be

\dfrac{25}{100}\times x\\\\=0.25x

Amount after marked down becomes

x-0.25x\\\\=0.75x

Additional clearance items by 40% off

Amount of additional off is given by

\dfrac{40}{100}\times 0.75x\\\\=0.4\times 0.75x\\\\=0.3x

After additional off, the amount becomes,

0.75x-0.3x\\\\=0.45x

Hence, he would pay 45% of the original price.

5 0
3 years ago
Consider the sets A={1,3,5,7} and B={11,13,15,21}.
katovenus [111]
Those should be odd integers if I’m wrong let Me know and I’ll fix it for you
4 0
3 years ago
Help please will mark brainliest
ipn [44]

Answer:

459

Step-by-step explanation:

27 x 17= 459

3 0
2 years ago
Can you help me please
STALIN [3.7K]

Answer:

36

Step-by-step explanation:

Here we a given a rule

It say

x(y÷3)^2

And we are given the values of x and y as

x=4 and y = 9

Let us replace them in the rule we are provided with

4(9÷3)^2

Applying DMAS rule, which says, first Division ollowed by Multiplication addition and then subtraction .

We first divide 9 by 3

9÷3 = 3

Hence

4(9÷3)^2 = 4(3)^2

Now we square first

3^2 = 3 \times 3 = 9

4(3)^2 = 4 \times 9

4(3)^2 = 36

Hence our final answer will be 36

4 0
3 years ago
Y= 5x - 9; domain = { 1,3,7 }<br> what is the range values?
Maslowich

Answer:

Step-by-step explanation:

range = [-4,6,26]

Step-by-step explanation:

y = 5x - 9.....domain = [1,3,7]....the domain is ur x values, and I am assuming ur looking for the y values that go with the x ones

y = 5x - 9.....when ur domain (ur x) = 1

y = 5(1) - 9

y = 5 - 9

y = -4

y = 5x - 9...when ur domain (x) = 3

y = 5(3) - 9

y = 15 - 9

y = 6

y = 5x - 9...when ur domain(x) is 7

y = 5(7) - 9

y = 35 - 9

y = 26

so ur range (ur y valus) = [-4,6,26]

6 0
3 years ago
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