Quadratic Function – Mathematica Education

What is the meaning of function? If you count it has the shape of the equation y = f (X) Can be said as Y is a function of XIf there is a connection between the X variable and the variable y is so similar that for each x obtained exactly a y. Confused? Simply a function is a relationship that translates the relationship between x and y. He connects every X exactly with every y. If the relationship involves square operations, then it is called the quadratic function.

Functional value y = f (X) If X = X₁ Lay Yer Yief and₁ = f (X₁). So X₁ and y₁ is a coordinate point pair that compiles the graph of function y = f (X).

Square function

The general form of quadratic function is

F (X) = aX² + bX + C or
y = aX² + bX + c

In addition to writing quadratic functions as above, there are other writing in form

• Mapping Form: R -> R
  x -> ax2 + bx + c, a, b, c ∈ R, a ≠ 0
• B. Forms of Collection {(x, y) iy = aX² + bX + C; A, b, c ∈ Real a ≠ 0

Quadratic function graph

In high school, you often encounter about the graph of quadratic functions. Usually the questions are struggling about extreme values, peak points, how the graph drawings, symmetry axes, and others. The name of the graph of the quadratic function is a graph with a satellite dish (such as a mountain or valley). To know how the graphic form of a quadratic function, you must pay attention to some of the important traits of the quadratic function below.

1. Relationship with the Y axis (if x = 0)

If from the equation y = aX² + bX + C We enter x = 0 then you will find y = c. So the satellite dish point with the Y axis is the point with coordinates (0, C).

2. Relationship with the x axis (y = 0)

From form aX² + bX + C If y = 0 it will produce a quadratic equation aX² + bX + C = 0, from this equation the value of D (discriminant) d = B2-4AC.

1. If the value of D> 0, then the parabola cuts the x axis at two different points.
2. If the value d = 0, then the parabola cuts the x axis at one point or it can be said to be a parabolic (graph of quadratic function) offending the x axis (peak point)
3. If d <0, then the parabola does not cut on the x axis (floating above or below the x axis)

• In the case d < 0 dan a > 0 then f (X) = aX² + bX + C, will produce a always positive value (floating above the x axis)
• In terms of <0 and a <0 then f (X) = aX² + bX + C, will produce a always negative value (floating under the x axis)

3. Extreme prices and peak points

formula determining extreme prices

(xp, yp) = (-b/2a, d/4a)

To find out whether it is the minimum or maximum point depends on the value a. If A> 0 then maximum, if A <0 then the minimum value.

The top point From the quadratic function f (X) = aX² + bX + C is the point obtained by taking coordinates from the extreme pair with its abscissa. The peak coordinates of the quadratic function are the point P (-b/2a, D/4a). Point P is called maximum if A> 0 and is called the minimum point if A <0.

4. Symmetry axis

The symmetry axis is a line that is drawn from the X extreme point parallel to the Y axis which divides the satellite dish into 2 equal parts.

The equation for symmetrical axes is X = -B/2a