write your answer in the form a(x - h)^2 + k, where a, h, and k are integers or simplified fractions. g(x) =

Explanation:

Step1: Identify vertex

The vertex of the parabola is at $(h,k)=(0,1)$.

Step2: Use a point on the parabola

Let's use the point $(1,2)$ on the parabola. Substitute $x = 1$, $y=2$, $h = 0$, $k = 1$ into $y=a(x - h)^2+k$. We get $2=a(1 - 0)^2+1$.

Step3: Solve for a

$2=a\times1^2 + 1$, which simplifies to $2=a + 1$. Subtracting 1 from both sides gives $a=1$.

Step4: Write the equation

Substitute $a = 1$, $h = 0$, $k = 1$ into $a(x - h)^2+k$. The equation is $1(x - 0)^2+1$.

Answer:

$1(x - 0)^2+1$