write an equation for the function given. use f(x) for the functions name. 9) 10)

write an equation for the function given. use f(x) for the functions name. 9) 10)

write an equation for the function given. use f(x) for the functions name. 9) 10)

Answer

Explanation:

Step1: Identify the general form of a quadratic function

The general form of a quadratic function is $f(x)=a(x - h)^2 + k$, where $(h,k)$ is the vertex of the parabola.

Step2: Analyze the first graph (9)

The vertex of the parabola in graph 9 is $(2, 0)$. So $h = 2$ and $k=0$. The parabola opens down - ward, so $a<0$. Let's assume $a=-1$. Then the function is $f(x)=-(x - 2)^2$. Expanding it gives $f(x)=-(x^{2}-4x + 4)=-x^{2}+4x - 4$.

Step3: Analyze the second graph (10)

The vertex of the parabola in graph 10 is $(-1,-2)$. So $h=-1$ and $k = - 2$. The parabola opens upward, so $a>0$. Let's assume $a = 1$. Then the function is $f(x)=(x + 1)^2-2$. Expanding it gives $f(x)=x^{2}+2x+1 - 2=x^{2}+2x - 1$.

Answer:

  1. $f(x)=-x^{2}+4x - 4$
  2. $f(x)=x^{2}+2x - 1$