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.
     • The red line shows the axis of symmetry on the parabola

2. vertex

   • A 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.

3. parabola

   • a symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity ideally follows a curve of this shape.

4. minimum

   • The minimum of a set of numbers is the smallest one.
     • The minimum of {3,2,8,1,9,2} is 1.
   • The lowest point on a graph.

5. maximum

   • The maximum of a set of numbers is the biggest one.
     • The maximum of {3,2,8,1,9,2} is 9.
   • The highest point on a graph.

6. x-intercept

   • A point at which a graph intersects the x-axis. The x-intercepts of a function must be real numbers, unlike roots and zeros.
     • the x-intercept of this graph is 5

7. y-intercept

   • A point at which a graph intersects the y-axis.
     • The y-intercept of this graph is 1

8. zeros of the function

   • an input value that produces an output of zero (0)
     • the zeros of this function are negative one and three because they make an output of zero

9. roots of the equation

   • A solution to an equation of the form f(x) = 0. Roots may be real or complex.
     • The roots of f(x) = 0 are the same as the zeros of the function f(x). Sometimes in casual usage the words root and zero are used interchangeably.

10. 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.

11. discriminant

    • The discriminant is the name given to the expression that appears under the square root (radical) sign in the quadratic formula.

12. difference of squares

    • the difference of two squares is a squared (multiplied by itself) number subtracted from another squared number. Every difference of squares may be factored according to the identity
      • a^2-b^2 = (a+b)(a-b)

13. perfect square trinomial

    • A perfect square binomial is a trinomial that when factored gives you the square of a binomial
      • x^2 + 2xy + y^2 is a perfect square binomial because it factors to (x + y)^2.

14. factors of a quadratic

    • to factor a quadratic is to find what to multiply to get the Quadratic
      • The factors of x2 + 3x − 4 are: (x+4) and (x−1)

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