fill in the equation for this function.\ny = ?(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: Find the vertex

From the graph, the vertex of the parabola is at the point $(0, - 2)$. So, $h = 0$ and $k=-2$.

Step3: Find the value of a

The parabola passes through the point $(1,2)$. Substitute $x = 1$, $y = 2$, $h = 0$ and $k=-2$ into $y=a(x - h)^2 + k$. We get $2=a(1 - 0)^2-2$. Simplify the equation: $2=a - 2$. Add 2 to both sides: $a=4$.

Answer:

$y = 4(x - 0)^2-2$