Steps To Draw Graph of Quadratic Function

Steps to draw graph of y=ax²+bx+c as follows:

1. Determine absis intersection, y = 0
2. Determine ordinat intersection, x = 0
3. Determine equation of axis of symmetry, x = -b/2a
4. Determine maximum or minimum value, y = (b²-4ac)/4a
5. Determine coordinate of extreme point, (x,y) = (-b/2a,(b²-4ac)/4a)
6. If 5 steps above have not drawn parabola sketch yet, then get some auxiliary point

Example:

Draw graph of equation y=x²-4x-5

1. Determine absis intersection
   y = 0 then:
   y = x²-4x-5
   (x-5) (x+1) = 0
   x₁ = -1 dan x₂ = 5
   then absis intersection are (-1,0) dan (5,0)
   


2. Determine ordinat intersection
   x = 0 then:
   y = 0²-4(0)-5
   y = -5
   then ordinat intersection is (0,-5)
   


3. Determine equation of axis of symmetry
   x = -b/2a
   x = -(-4)/2(1)
   x = 2
   axis of symmetry is line x = 2
   


4. Determine maximum or minimum value
   y = (b²-4ac)/-4a
   y = ((-4)²-4(1)(-5))/-4(1)
   y = -9
   


5. Extreme pointk:
   (-b/2a,(b²-4ac)/4a)
   (-(-4)/2(1),((-4)²-4(1)(-5)/4(1))
   (4/2,36/4)
   (2,9)
   
6. Connect points are gotten
   

Source:
http://lucudankyut.blogspot.com

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