The graphs of quadratic functions,  f (x) = ax2 + bx + c, are called parabolas.

 Shape of the Graph: Parabolas have a shape that resembles (but is not quite the same as) the letter U. Parabolas may open upward or downward. If the sign of the leading coefficient, a, is positive (a > 0), the parabola opens upward. If the sign of the leading coefficient, a, is negative (a < 0), the parabola opens downward.

 Parts of the Graph: The bottom (or top) of the U is called the vertex, or the turning point. The vertex of a parabola opening upward is also called the minimum point. The vertex of a parabola opening downward is also called the maximum point. The x-intercepts are called the roots, or the zeros. To find the x-intercepts, set ax2 + bx + c = 0. The ends of the graph continue to positive infinity (or negative infinity) unless the domain (the x's to be graphed) is otherwise specified.

Axis of Symmetry:
The parabola is symmetric (a mirror image) about a vertical line drawn through its vertex (turning point). This line is called the axis of symmetry. The equation for the axis of symmetry is .
 Parabola:   y = x2 + 4x - 5 Axis of symmetry: x = -2 Determine the coordinates of the "vertex" (the minimum point in this graph) by substituting the x = -2 into the equation. y = (-2)2 + 4(-2) - 5 y = 4 - 8 - 5 y = -9 Vertex: (-2,-9) Parabola:   y = -x2 + x + 6 Axis of symmetry: Determine the coordinates of the "vertex" (the maximum point in this graph) by substituting the x = ½ into the equation. y = -(½)2 + ½ + 6 y = -¼ + ½ + 6 y = 6¼ Vertex: (½, 6¼)