fill in the equation for this function. y = ?(x - )^2+

Explanation:

Step1: Identify vertex form of parabola

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

Step2: Locate the vertex

From the graph, the vertex of the parabola is at the point $(1,2)$. So, $h = 1$ and $k=2$.

Step3: Find the value of $a$

The parabola passes through the point $(2,0)$. Substitute $x = 2$, $y = 0$, $h = 1$ and $k = 2$ into $y=a(x - h)^2 + k$. We get $0=a(2 - 1)^2+2$, which simplifies to $0=a + 2$. Solving for $a$, we subtract 2 from both sides: $a=-2$.

Answer:

$y=-2(x - 1)^2+2$