Parabolas

Hello everyone,

This is professor Lana Shash and today we are going to look over quadratic functions or also known as parabola.

Part 1:  We are going to look at what parabola's are :

• Graph of a quadratic function which is a U shape 
• General equation : y=ax2+bx+c
• Downward or upward movement 
• Examples : y= x2 -2x+6
• Real life examples : Graphing the flight of a baseball 

                   Part 2: We will look at the characteristics of a parabola

1.                                     If the leading coefficient of a in the general equation is negative, then the graph is concave down and there is a maximum values
2.                                     If the leading coefficient is positive then the graph is concave up and there is a minimum value
3.       p             All  parabolas have a vertical symmetry    

                           

                   Part 3: I will explain how we calculate the vertex :

1. Pa               The equation to calculate the vertex : -b/2a
2.                     To find the value b and a, we need to look into the general equation y=ax²+bx+c
3. ni 

                     Part 4: We will look at the different forms we can express a quadratic function :

1.                                    Standard and general form: f(x)=ax²+bx+c
2.                                    Vertex form : g(x) = a(x-h)² + k, where (h;k) is the vertex
3.                                     Factored form : b(x) = a(x-r)(x-s) where r and s are the x-intercept

                      Part 5: I will explain how to find the y and x intercept : 

1.                    X-intercept: replace the y-value by 0 in the general equation which will give you the x-value. When the function is not factorable, we can use the quadratic formula.  
2.                                     Y-intercept: replace the x-value by 0
3.                      Example : y= x²-x- 6 --> y-int : when x=0 ; y=-6 and x-int :x²-x-6 = (x-3)(x+2) --> x=3 or x=2

                                                         

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