Question

How do I do I calculate the curve of best fit with the following data points given?

Answer 1

To determine the curve of best fit, let's look at the x-intercepts of the curve.

Based on the graph, the x-intercepts are at x = -7 and x = -1.

Since -7 and -1 are the x-intercepts, we can say that the factors of this curve are:

`(x+7)(x+1)`

Now, we can also see that the graph is opening downward, therefore, the leading coefficient of the equation of this graph must be negative. For this, we will multiply the factors above by -1.

`-(x+7)(x+1)`

All we have to do now is multiply the factors above in order to get the curve of best fit.

`-(x^2+x+7x+7)`

Combine similar terms like x and 7x.

`-(x^2+8x+7)`

Then, distribute the negative sign.

`-x^2-8x-7`

Therefore, the curve of best fit is y = -x² - 8x - 7.