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3 years ago

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:

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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4 times 2 1/8 mixed number in simpileest form

Anuta_ua [19.1K]

Answer:

8.5

Step-by-step explanation:

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3 years ago

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Drag each expression to the correct location on the model. Not all will be used

grandymaker [24]

Answer: $\dfrac{x^{2}+2x+1 }{\mathbf {x-1}} \cdot \dfrac{\mathbf {5x^{2} +15x-20} }{7x^{2} +7x}$

Step-by-step explanation:

$\dfrac{\dfrac{5x^{2} +25x+20}{7x} }{\dfrac{x^{2} +2x+1}{7x^{2} +7x} } =\dfrac{5x^{2} +25x+20}{7x} \times \dfrac{7x^{2} +7x}{x^{2} +2x+1}=\dfrac{5x^{2} +25x+20}{7x} \times \dfrac{7x(x +1)}{(x+1)^{2} }=\\\\=\dfrac{5x^{2} +25x+20}{x+1} =\dfrac{{5(x+1)(x+4)}}{x+1}=5(x+4)$

$5(x+4)=\dfrac{5(x-1) \cdot (x+4)}{x-1}=\dfrac{5x^{2} +15x-20}{x-1}$

<em>Thus, the expressions will be used: (5x² + 15x - 20) and (x + 4).</em>

<em>Let's check:</em>

$\dfrac{x^{2}+2x+1 }{\mathbf {x-1}} \cdot \dfrac{\mathbf {5x^{2} +15x-20} }{7x^{2} +7x} =\dfrac{(x+1)^{2} }{x-1} \cdot \dfrac{5(x-1) \cdot (x+4)}{7x(x+1)} =\\\\=\dfrac{(x+1) \cdot 5 \cdot (x+4)}{7x} =\dfrac{5x^{2} +25x+20}{7x}$

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3 years ago

One night, it is 24LaTeX: ^\circ

tatuchka [14]

Answer:

$T^\circ = -12^\circ$

Step-by-step explanation:

Given

Represent the temperature in Tucson with T and that in Minneapolis with M.

From the first statement, we have:

$T^\circ = M^\circ - 24^\circ$

From the second, we have:

$T^\circ = -M^\circ$ or $M^\circ = -T^\circ$ --- i.e. both are opposite numbers

Required

Find T

To calculate T, substitute -T for M in $T^\circ = M^\circ - 24^\circ$

This gives:

$T^\circ = -T^\circ - 24^\circ$

Collect Like Terms

$T^\circ +T^\circ =- 24^\circ$

$2T^\circ =- 24^\circ$

Make T the subject

$T^\circ =- 24^\circ/2$

$T^\circ = -12^\circ$

Hence, the temperature in Tucson is $-12^\circ$

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3 years ago

Write a polynomial function in factored form with double roots at -2 and 5 and the constant term of the polynomial in standard f

Amanda [17]

Answer:

$f(x)=-0.4x^4+2.4x^3+8.4x^2-24x-40$

Step-by-step explanation:

If -2 and 5 are double roots of the polynomial function, then the function expression is

$f(x)=a(x-(-2))^2(x-5)^2\\ \\f(x)=a(x+2)^2(x-5)^2$

Rewrite this function in standard form:

$f(x)=a(x^2+4x+4)(x^2-10x+25)\\ \\f(x)=a(x^4-10x^3+15x^2+4x^3-40x^2+100x+4x^2-40x+100)\\ \\f(x)=a(x^4-6x^3-21x^2+60x+100)\\ \\f(x)=ax^4-6ax^3-21ax^2+60ax+100a$

The constant term of the polynomial in standard form is -40, so

$100a=-40\\ \\a=-\dfrac{40}{100}=-0.4$

Therefore, the function expression is

$f(x)=-0.4x^4-6\cdot (-0.4)x^3-21\cdot (-0.4)x^2+60\cdot (-0.4)x+100\cdot (-0.4)\\ \\f(x)=-0.4x^4+2.4x^3+8.4x^2-24x-40$

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4 years ago

A boy weighing blank kilograms is riding a skateboard. He’s moving at 2 meters/second and has 40 joules of kinetic energy. He do

Ira Lisetskai [31]

Answer:

His kinetic energy at the faster speed is 160 J

Step-by-step explanation:

Here in this question, we are interested in calculating the kinetic energy at the faster speed.

Firstly, we need to know the mass of the boy’s body. We can do this by using the kinetic energy formula;

Mathematically;

K.E = 1/2 * m * v^2

From the question;

K.E = 40 Joules

m = ?

v = speed = 2 m/s

Now, plugging these values into the kinetic energy equation, we have;

40 = 1/2 * m * 2^2

40 = 1/2 * m * 4

40 = 4m/2

4m = 40 * 2

4m = 80

m = 80/4

m = 20 kg

Now that we know the mass of the boy’s body, we can proceed to calculate the new K.E

Let’s follow the third statement in the question;

We were told that he doubles his speed upon sighting his friend.

Recall, he was traveling at a speed of 2 m/s.

Now doubling this means the new speed will

be 2 * 2 = 4 m/s

Now, we want to calculate the kinetic energy value at this new speed.

Mathematically, we use the same formula for kinetic energy.

K.E = 1/2 * m * v^2

We know that m is the mass that we calculated as 20kg and our v here is 4 m/s

Plugging these values, we have;

K.E = 1/2 * 20 * 4^2

K.E = (20 * 16)/2

K.E = 320/2

K.E = 160 J

6 0

3 years ago

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