what function models the data shown on the graph?\n○ (f(x)=2(x - 5)(x - 1))\n○ (f(x)=-2(x - 5)(x - 1))\n○…

what function models the data shown on the graph?\n○ (f(x)=2(x - 5)(x - 1))\n○ (f(x)=-2(x - 5)(x - 1))\n○ (f(x)=2(x + 5)(x + 1))\n○ (f(x)=-2(x + 5)(x + 1))

what function models the data shown on the graph?\n○ (f(x)=2(x - 5)(x - 1))\n○ (f(x)=-2(x - 5)(x - 1))\n○ (f(x)=2(x + 5)(x + 1))\n○ (f(x)=-2(x + 5)(x + 1))

Answer

Answer:

B. $f(x)=-2(x - 5)(x - 1)$

Explanation:

Step1: Identify x - intercepts

The x - intercepts of the graph are at $x = 1$ and $x=5$. So the factored form of the quadratic function is $y=a(x - 1)(x - 5)$.

Step2: Determine the value of a

The parabola opens downwards, so $a<0$. Among the options with factors $(x - 1)(x - 5)$, the function with a negative leading - coefficient is $y=-2(x - 5)(x - 1)$.