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

3432532

step-by-step explanation:

Answer from: Quest

y=mx+b

step-by-step explanation:

m slope

b y-intercept

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