The Role of Coefficients in Quadratic Curves

The general equation of a quadratic curve isEach the coefficnetsandhas a different role in determining the shape and position of the curve.

(or the point with coordinates)is the intercept of the curve with the y – axis. The intercept is the value of y for which x=0.

determines the 'width' of the curve, or the degree of horizontal stretch.

anddefine a line of symmetric with equation

andtogether determine the minimum or maximum point of the curve, also called the vertex. Ifthe vertex is a minimum. Ifthe vertex is a maximum. For the general quadraticthe vertex is at

Example: Ifthe– intercept is atthere is a line of symmetry with equationand the vertex is at the pointor