Question

Which of the following functions best models the data represented by the scatterplot shown below?

Answer 1

Let's take random data points from the graph:

(x, y) ==> (5, 210), (9, 650), (13, 1400), (19, 3000)

Let's select the best function that models the data represented by the scatter plot.

Let's start from the first function.

`y=8x^2+10`

Input the values of x and verify if the function gives the corresponding value for y.

• When x = 5:

`\begin{gathered} y=8(5)^2+10 \\ y=200+10 \\ y=210 \end{gathered}`

• When x = 9:

`\begin{gathered} y=8(9)^2+10 \\ y=648+10 \\ y=650 \end{gathered}`

• When x = 19:

`\begin{gathered} y=8(19)^2+10 \\ y=2888+10 \\ y=2898\approx3000 \end{gathered}`

We can see the equation gives the estimated values of y for each value of x as shown in the graph.

Therefore, the function which best models the data represented by the scatterplot is:

`y=8x^2+10`

ANSWER:

`y=8x^2+10`