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Question

8bithelix · Answer

@563blackghost

563blackghost · Answer

You would split the equation down the middle.

$\bf{(x^{2}-4x)+(9x-36)}$

Next you need to factor out `x` and `9` from the equation.

$\bf{x(x-4)+9(x-4)}$

Now you have common terms. You would factor these out as well.

$\bf{x=4,-9}$

563blackghost · Answer

For 4: Use this table to figure out the tranformation that is occuring.

563blackghost · Answer

Do you have an idea what the translation could be for 4?

563blackghost · Answer

Use the same table for question 5.

|dw:1521671777913:dw|

563blackghost · Answer

A quadriatic function format is:

$\large\bf{y=x^{2}}$

There are 3 types of transformations: Translation, Reflection, and Dilation.

~

For translation there is a `vertical` or `horizontal` shift.

If your equation moves `vertically up` it's format changes to $\bf{y=x^{2}+k}$.

If your equation moves `vertically down` it's format changes to $\bf{y=x^{2}-k}$.
`VERTICAL TRANSFORMATIONS ARE NOT CONTAINED IN PARENTHESIS!`

If your equation moves `horizontal right` it's format changes to $\bf{y=(x-h)^{2}}$.

If your equation moves `horizontal left` it's format changes to $\bf{y=(x+h)^{2}}$.

`HORIZONTAL TRANSFORMATION ARE CONTAINED WITHIN PARENTHESIS!`

~~~

Dilation can be a compression or a stretch.

They are represented as: $\bf{y=ax^{2}}$

If the scaling is `larger than 1` then it is an `stretch`.

If the scaling is `less than 1` then it is a `compression`.

~~~

Reflection would resort in a negative.

~~~

8bithelix · Answer

ah ok

563blackghost · Answer

In your equation you have:

$\large\bf{f(x)=4x^{2}+5}$

You see already that you have +5, this means that there is a `vertical translation of 5`.

You also see that `4` is `multiplied` with $\bf{x^{2}}$, this means that there is a stretch of the function. `BECAUSE 4 IS GREATER THAN 1`.

Now your question asks for a `translation of 4 units up`.

A translation that is vertical will not be contained in parenthesis, this means the format would be $\bf{y=x^{2}+k}$ due to a shift upward of 4.

So we apply..

$\large\bf{f(x)=4x^{2}+5 \color{red}{+4}}$

8bithelix · Answer

is now translated upwards

8bithelix · Answer

i guess..

8bithelix · Answer

dont mind my stupidity :/

563blackghost · Answer

yes the function is translating upward.

8bithelix · Answer

so i assume thats the g(x) equation

563blackghost · Answer

$\bf{g(x)=4x^{2}+5+4}$ is g(x).