Additional Mathematics

SKETCHING QUADRATIC GRAPH

Ex: f(x)² = x²-10x-11

1. a=1 a>0 (minimum graph)

2. b²-4ac = (-10)² -4(1)(-11)

= 144


b²-4ac > 0

graph intersects at 2 point at x-axis

3. Let f(x) = 0

x²-10x-11 = 0

(x+1) (x-11) = 0



x = -1 x = 11



4. Finding the y intercept

f(x) = x² - 10x -11

Let x = 0

f(x) = -11



5. Completing the square

f(x) = x² -10x-11

= x²- 10x + (10/2)² - (10/2)² - 11

= (x-5)² - 36



x-5 = 0

x = 5