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