10.01 Vocabulary - Unit 10

Quadratic Formula

he quadratic formula is a formula that provides the solution to a quadratic equation. There are other ways of solving a quadratic equation instead of using the quadratic formula, such as factoring, completing the square, graphing and others

Completing the Square

In elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form to the form for some values of h and k.

Axis of Symmetry

The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves

Vertex

The common endpoint of two or more rays or line segments. Vertex typically means a corner or a point where lines meet.

Root of an Equation

The roots of a function are the x-intercepts. By definition, the y-coordinate of points lying on the x-axis is zero.

Maximum

a point at which a function's value is greatest.

Parabola

is a curve where any point is at an equal distance from: a fixed point (the focus ), and. a fixed straight line (the directrix )

Quadratic Equation

is any equation that can be rearranged in standard form as where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0. If a = 0, then the equation is linear, not quadratic, as there is no term.

Zero of a Function

is any replacement for the variable that will produce an answer of zero. Graphically, the real zero of a function is where the graph of the function crosses the x‐axis; that is, the real zero of a function is the x‐intercept(s) of the graph of the function.

Quadratic Function

is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in "width" or "steepness", but they all have the same basic "U" shape.

Minimum

point at which the value of a function is less than or equal to the value at any nearby point

Discriminant

the discriminant of a polynomial is a quantity that depends on the coefficients and determines various properties of the roots. The discriminant of a polynomial is generally defined in terms of a polynomial function of its coefficients.