Question

Write the equation for f(x)=x^2

Answer 1

Answer:

$f^\prime(x)=-(x+1)^2-4$

Step-by-step explanation:

We have the function:

$f(x)=x^2$

And we want to write its equation after being: 1) Flipped over the x-axis, 2) shifted 4 units down, and 3) shifted 1 unit to the left.

To denote a flip over the x-axis, we multiply the function by -1. Hence:

$f^\prime(x)=-x^2$

Is our function flipped over the x-axis.

To shift n units vertically, we simply add n to our function.

Since we are going 4 units downwards, we will add -4 to our function. Hence:

$f^\prime(x)=-x^2-4$

Finally, to shift n units horizontally, we substitute our variable $x$ for $(x-n)$.

Since we are shifting 1 unit to the left, n=-1. Hence, we will substitute $x$ for $(x+1)$. Therefore:

$f^\prime(x)=-(x+1)^2-4$

So, our final function is:

$f^\prime(x)=-(x+1)^2-4$