Quadratic Vocabulary

Quadratic Vocabulary

1. Axis of Symmetry: A line of symmetry for a graph. The two sides of a graph on either side of the axis of symmetry look like mirror images of each other.

   • Parabola: A u-shaped curve with certain specific properties. Formally, a parabola is defined as follows: For a given point, called the focus, and a given line not through the focus, called the directrix, a parabola is the locus of points such that the distance to the focus equals the distance to the directrix.
   • Maximum: To find the largest possible value.
   • Y-intercept: A point at which a graph intersects the y-axis.
     • Roots of the equation: A solution to an equation of the form f(x) = 0. Roots may be real or complex.
     • Discriminant: The number D = b2 – 4ac determined from the coefficients of the equation ax2 + bx + c = 0. The discriminant reveals what type of roots the equation has.

2. Vertex: corner point of a geometric figure. For a polygon, vertices are where adjacent sides meet. For an angle, the vertex is where the two rays making up the angle meet. tex:

   • Minimum: Either a relative (local) minimum or an absolute (global) minimum.
   • X-intercepts: A point at which a graph intersects the x-axis. The x-intercepts of a function must be real numbers, unlike roots and zeros.
   • Zeros of the function: A value of x which makes a function f(x) equal 0. A zero may be real or complex.
     • End behavior: The appearance of a graph as it is followed farther and farther in either direction. For polynomials, the end behavior is indicated by drawing the positions of the arms of the graph, which may be pointed up or down. Other graphs may also have end behavior indicated in terms of the arms, or in terms of asymptotes or limits.
     • ifference of squares: An equation showing a relationship between a function and its derivative(s).