A.ST.1: Finding curve of best fit using Quadratic Model-12/3/24

A quadratic function is a polynomial function of degree 2, typically written in the form $$y = ax^2 + bx + c$$ , where $$a$$ , $$b$$ , and $$c$$ are constants and @@a eq 0@@.

The curve of best fit is a line or curve that best represents the data points in a scatter plot, minimizing the distance between the data points and the curve.

You can use methods such as regression analysis to find the coefficients $$a$$ , $$b$$ , and $$c$$ in the quadratic equation $$y = ax^2 + bx + c$$ that best fit the data.

The vertex is the highest or lowest point on the graph of a quadratic function, located at the point $$(h, k)$$ , where $$h = -\frac{b}{2a}$$ and $$k = f(h)$$ .

The coefficient 'a' determines the direction of the parabola: if $$a > 0$$ , the parabola opens upwards; if $$a < 0$$ , it opens downwards.

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation $$x = -\frac{b}{2a}$$ .

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

Linear functions have a constant rate of change and are represented by a straight line, while quadratic functions have a variable rate of change and are represented by a parabola.

If the second differences of the y-values are constant, the relationship is quadratic.

The general form of a quadratic equation is $$Ax^2 + Bx + C = 0$$ , where $$A$$ , $$B$$ , and $$C$$ are constants.