Question

F(x) = 2(x - -1)^2+2

Answer 1

Answer:

The simplified form is: $2x^2+4x+4$

Step-by-step explanation:

Here we are asked to find the simplified form for the function:

$f(x) = 2(x - (-1))^2+2$

So, we just need to expand it by applying the formula:

$\left(a+b\right)^2=a^2+2ab+b^2$

Now, the given expression is also re-written as:

$f(x) = 2(x - (-1))^2+2$

$=2\left(x+1\right)^2+2$

So on expanding, we have:

$2\left(x+1\right)^2+2$

$=2\left(x^2+2x+1\right)+2\\=2x^2+2\cdot \:2x+2\cdot \:1+2\\=2x^2+4x+4$

So we have the simplified form, as given.