the graph shows the axis of symmetry for a quadratic function f(x). which could be the function? f(x)=(x +…

the graph shows the axis of symmetry for a quadratic function f(x). which could be the function? f(x)=(x + 4)^2 f(x)=x^2 + 4 f(x)=(x - 4)^2 f(x)=x^2 - 4

the graph shows the axis of symmetry for a quadratic function f(x). which could be the function? f(x)=(x + 4)^2 f(x)=x^2 + 4 f(x)=(x - 4)^2 f(x)=x^2 - 4

Answer

Explanation:

Step1: Recall axis - of - symmetry formula

For a quadratic function in vertex form $f(x)=a(x - h)^2 + k$, the axis of symmetry is $x = h$.

Step2: Analyze each option

  • For $f(x)=(x + 4)^2=(x-(-4))^2+0$, the axis of symmetry is $x=-4$.
  • For $f(x)=x^2 + 4=(x - 0)^2+4$, the axis of symmetry is $x = 0$.
  • For $f(x)=(x - 4)^2$, the axis of symmetry is $x = 4$.
  • For $f(x)=x^2-4=(x - 0)^2-4$, the axis of symmetry is $x = 0$.

Answer:

If the axis of symmetry is $x = 4$, the function is $f(x)=(x - 4)^2$. So the answer is $f(x)=(x - 4)^2$.