Quadratic Functions
Quadratic function is a function of second degree in one variable. There are three commonly used forms of quadratic functions.
Standard or general form : 
Factored form – x-intercept form : 
Vertex form : 
Each form can be converted to another form of quadratic function easily.
Domain of a quadratic function is the set of all x-values, but range of a quadratic function is the set of y-values that the function results in. Range of a quadratic function easily determined by graphing functions. Graph of a quadratic function is called parabola. Vertex of parabola is turning point, where horizontal tangent occurs. The y value of vertex of a quadratic equation is maximum or minimum value of function. After identifying vertex of quadratic function, it is easy to determine the range. Range can be negative infinity to maximum point or can be minimum point to positive infinity.
Vertex of a quadratic function is at point V(h, k). The values of h and k are seen in vertex form. x=h is called axis of symmetry. x-coordinate of a quadratic functions’ vertex is equal to
or 
y-coordinate of a quadratic functions’ vertex is equal to
While graphing a quadratic function, first step is examining the sign of constant a. If coefficient of x2 in quadratic function is positive, then legs of parabola will be upward. If coefficient of x2 in quadratic function is negative, then legs of parabola will be downward.
Second step is determining the y-intercept of quadratic function. When you input 0 to x then you can find the y-intercept of quadratic function.
Third step is determining the x-intercept of quadratic function. When you equalize quadratic function to 0 and then find x values you determine the x-intercept of quadratic function. The quadratic function equals to zero is quadratic equation.
Fourth step is determining the vertex point.
To solve a quadratic equation there is 3 methods.
1. Factorizing
2. Completing Square
3. Formula
Before factorizing rearrange quadratic equation into the form 
. Zero must be on one side and it is easier to use the side where a is positive.
As we know from binomial theorem 
. If we rearrange standard form of the quadratic equation to vertex form of quadratic equation, you can easily identify the roots/zeros.
Quadratic formula is used first finding discriminant of quadratic equations. It is denoted by 
.
Roots/zeros of quadratic function is equal to
As discriminant of quadratic equation will be in the second root it cannot be negative. And when discriminant of quadratic equation is 0 then the values of root will be equal.
Summation of details of discriminant is;
When 
then quadratic equation has two distinct real roots
When 
then quadratic equation has two equal real roots. (double root)
When 
then quadratic equation has no real roots (imaginary roots)
In IB Math AA syllables Functions seen at
IB Math SL AA Topic 2 Quadratic Functions
IB Math HL AA Topic 2 Quadratic Functions
The formula for axis of symmetry of quadratic function, solutions of a quadratic equation and discriminant of a quadratic equation is given in IB Math SL DataBooklet. (data booklet a link verebiliriz).
EduIB Questionbank gives you opportunity to solve real past paper like questions about Functions, Quadratic Functions, Transformations of Function and Rational Functions. (sorulara link verebiliriz)
For example one of Quadratic Functions in EduIB is shown below. It is very similar to IB Math SL Exam in November 2013.
