Quadratics/Line of Best Fit/Curve of Best Fit Practice

A quadratic function is a polynomial function of degree 2, typically in the form of $$f(x) = ax^2 + bx + c$$ , where a, b, and c are constants and a ≠ 0.

The zeros of a quadratic function are the values of x for which the function equals zero. They can be found by solving the equation $$ax^2 + bx + c = 0$$ .

The number of zeros can be determined using the discriminant, $$D = b^2 - 4ac$$ . If D > 0, there are 2 distinct zeros; if D = 0, there is 1 zero; if D < 0, there are no real zeros.

The vertex is the highest or lowest point of the parabola represented by the quadratic function. It can be found using the formula $$x = -\frac{b}{2a}$$ .

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. It can be found at $$x = -\frac{b}{2a}$$ .

The line of best fit represents the trend of the data points in a scatter plot, showing the relationship between the independent and dependent variables.

The equation of the line of best fit can be found using linear regression, which calculates the slope and y-intercept based on the data points.

A curve of best fit is used to model data that does not follow a linear pattern, allowing for better predictions and understanding of the relationship between variables.

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

The factored form of a quadratic equation is $$y = a(x - r_1)(x - r_2)$$ , where $$r_1$$ and $$r_2$$ are the zeros of the function.