Answer:
I apologize, due to some urgent matters I wont be able to make the corrections to my answer.
To create a perfect square trinomial, halve the x coefficient, square it, and then add that value.
In the case of x² + 6x, we would have 6 to get 3, then square 3 to get 9.
We would add 9 to make a perfect square trinomial.
<u>
</u><u>Why this works</u>
A perfect square trinomial is designed to factor to some value (x+n)².
When you FOIL this you get x² + 2nx + n².
As you can see, if you wanted to find the value of that n², you could take that x coefficient 2n, halve it to get n, and then square it to get n²!
The rule for the reflection
rx-axis (x, y) → (x, –y)
ry-axis (x, y) → (–x, y)
<h3>Further explanation</h3>
A reflection is an example of a transformation
Reflection is the process of mirroring each point on the geometry of a certain line.
The original figure is called the pre-image and the final figure is called the image
The image will be congruent with the pre image and the distance of the image to the mirror axis is the same as the distance of the pre image to the mirror axis
There are several reflection equations:
- The equation of reflection across the<em><u> x-axis
</u></em>
x '= x
y '= - y
can be written
![\large{\boxed{\bold{r_{x-axis}A(x,y)\rightarrow A'(x,-y)}}](https://tex.z-dn.net/?f=%5Clarge%7B%5Cboxed%7B%5Cbold%7Br_%7Bx-axis%7DA%28x%2Cy%29%5Crightarrow%20A%27%28x%2C-y%29%7D%7D)
- The equation of reflection across the <u><em>y-axis
</em></u>
x '= x
y '= -y
can be written
![\large{\boxed{\bold{r_{y-axis}A(x,y)\rightarrow A'(x,-y)}}](https://tex.z-dn.net/?f=%5Clarge%7B%5Cboxed%7B%5Cbold%7Br_%7By-axis%7DA%28x%2Cy%29%5Crightarrow%20A%27%28x%2C-y%29%7D%7D)
- The reflection equation across the line <u><em>y = -x
</em></u>
x '= - y
y '= - x
can be written
![\large{\boxed{\bold{r_{y=-x}A(x,y)\rightarrow A'(-y,-x)}}](https://tex.z-dn.net/?f=%5Clarge%7B%5Cboxed%7B%5Cbold%7Br_%7By%3D-x%7DA%28x%2Cy%29%5Crightarrow%20A%27%28-y%2C-x%29%7D%7D)
- The reflection equation across the line x = h
x '= 2h-x
y '= y
can be written
![\large{\boxed{\bold{r_{x=h}A(x,y)\rightarrow A'(2h-x,y)}}](https://tex.z-dn.net/?f=%5Clarge%7B%5Cboxed%7B%5Cbold%7Br_%7Bx%3Dh%7DA%28x%2Cy%29%5Crightarrow%20A%27%282h-x%2Cy%29%7D%7D)
- The reflection equation across the line y = k
x '= x
y '= 2k-y
can be written
![\large{\boxed{\bold{r_{y=k}A(x,y)\rightarrow A'(x,2k-y)}}](https://tex.z-dn.net/?f=%5Clarge%7B%5Cboxed%7B%5Cbold%7Br_%7By%3Dk%7DA%28x%2Cy%29%5Crightarrow%20A%27%28x%2C2k-y%29%7D%7D)
So the correct rule for reflection is:
rx-axis (x, y) → (x, –y)
ry-axis (x, y) → (–x, y)
<h3>
Learn more</h3>
the rule for the reflection
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Keywords : reflection, y-axis