Mathematics: What is the axis of symmetry of f(x) = -3(x+1)to the power of 2 +12

What is the axis of symmetry of f(x) = -3(x+1)to - id315573610, quinnalbertson8643

Ответ:

frisha

21.01.2022

Analyzing the function

f(x) = -3(x+1)^2 +12

We can see that the "+12" at the end only causes a vertical translation, and thus won't change the axis of symmetry. So, it all comes down to find the axis of symmetry of

f(x) = -3(x+1)^2

But again, the "-3" coefficient in front only causes the parabola to be more or less narrow, and since it's negative, it reflects it across the axis. So, we can focus only on the part

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

The parent function f(x)=x^2 has the line x=0 (i.e. the axis) as the axis of symmetry. The child function f(x)=(x+1)^2 is obtained via a transformation like $f(x)\mapsto f(x+k)$ , which causes a horizontal translation, units to the left if is positive, units to the right if is negative. In this case, k=1 , so we translate the parent function one unit to the left, and the new axis of symmetry is x=-1