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

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

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

Answer

Explanation:

Step1: Recall axis - of - symmetry formula

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

Step2: Analyze each option

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

From the graph, the axis of symmetry is $x = 4$.

Answer:

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