Find the curve of best fit for a set of data

A curve of best fit is a mathematical function that best represents the relationship between a set of data points, minimizing the distance between the points and the curve.

A quadratic function is a polynomial function of degree 2, typically in the form of $$y = ax^2 + bx + c$$ , where a, b, and c are constants.

A quadratic model is appropriate if the data points show a parabolic trend, indicating that the relationship between the variables is not linear.

The general form of a quadratic equation is $$y = ax^2 + bx + c$$ .

The 'a' coefficient determines the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

The vertex of a parabola is the highest or lowest point on the graph, depending on the direction it opens.

The vertex can be found using the formula $$x = -\frac{b}{2a}$$ , and then substituting this value back into the function to find the corresponding y-coordinate.

The y-intercept is the point where the graph intersects the y-axis, which occurs when $$x = 0$$ . It is represented by the constant term 'c' in the equation.

Desmos is an online graphing calculator that allows users to input data points and find the curve of best fit by fitting various types of functions to the data.

Linear models represent relationships with a straight line, while quadratic models represent relationships with a parabolic curve, indicating a change in direction.