Mathematics, 19.02.2020 08:16 lopez7512

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

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Answer from: nhs5

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!

Answer from: daltondespain2

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

Answer from: Quest

spinning a 1, 2, or 3. option d.

step-by-step explanation: when spinning a number graph up to 4, and aiming for any number less than 3, that automatically eliminates the number 4. now you have two numbers to spin on that are less than 3, but the number 3 is included in this question because it's no greater of an number than itself. i hope this you : )

Answer from: Quest

step- i d k and i d c : )

you: : 0

bye

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