A quadratic function is a polynomial function of degree 2, with the general form f of x equals a x squared plus b x plus c, where a is not equal to zero. The coefficient a determines whether the parabola opens upward or downward and affects its width. The coefficient b affects the horizontal position of the parabola, while c represents the y-intercept. It's crucial that a is not zero, because if a equals zero, the function becomes linear rather than quadratic.
Now let's examine how each coefficient affects the parabola's appearance. The coefficient 'a' determines the parabola's opening direction and width. When a is positive, the parabola opens upward, and when a is negative, it opens downward. A larger absolute value of a makes the parabola narrower, while a smaller absolute value makes it wider. The coefficient 'b' affects the horizontal position by changing the axis of symmetry. Finally, coefficient 'c' creates a vertical shift, moving the entire parabola up or down, and represents the y-intercept where the parabola crosses the y-axis.