Question

the scatter - plot shows the relationship between two variables, x and y. which equation is the most appropriate quadratic model for the data shown?
a (y=(x - 11)^2+3)
b (y=(x - 3)^2+11)
c (y=(x + 3)^2-11)
d (y=(x + 11)^2-3)

Explanation:

Step1: Recall vertex - form of quadratic function

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

Step2: Estimate the vertex from the scatter - plot

By looking at the scatter - plot, we can estimate that the vertex of the parabola that best fits the data has an $x$ - coordinate around $3$ and a $y$ - coordinate around $11$.

Step3: Match the equation with the vertex

For the equation $y=(x - 3)^2+11$, the vertex is $(3,11)$.

Answer:

B. $y=(x - 3)^2+11$