1-1 Graphing Quadratic Functions Study Notes

Quadratic Function

A function expressed as $f(x) = ax^2 + bx + c$.

Coefficient a

The coefficient of the quadratic term ($x^2$). If $a > 0$, the parabola opens upward; if $a < 0$, it opens downward.

Coefficient b

The coefficient of the linear term ($x$).

Coefficient c

The constant term that represents the $y$-intercept of the function.

y-intercept

The value of the function when $x = 0$, equal to $c$.

Axis of Symmetry

The vertical line that divides the parabola into two symmetric halves, calculated using $x = -\frac{b}{2a}$.

Vertex

The highest or lowest point on the parabola, found using the axis of symmetry to determine the $x$-coordinate and substituting back into the function to find the $y$-coordinate.