Answer:
The simplified form is: [tex]2x^2+4x+4[/tex]
Step-by-step explanation:
Here we are asked to find the simplified form for the function:
[tex]f(x) = 2(x - (-1))^2+2[/tex]
So, we just need to expand it by applying the formula:
[tex]\left(a+b\right)^2=a^2+2ab+b^2[/tex]
Now, the given expression is also re-written as:
[tex]f(x) = 2(x - (-1))^2+2[/tex]
[tex]=2\left(x+1\right)^2+2[/tex]
So on expanding, we have:
[tex]2\left(x+1\right)^2+2[/tex]
[tex]=2\left(x^2+2x+1\right)+2\\=2x^2+2\cdot \:2x+2\cdot \:1+2\\=2x^2+4x+4[/tex]
So we have the simplified form, as given.
