Rucete ✏ Mathematics In a Nutshell
Cubic Function
The equation types
1. y = a(x-p)(x-q)(x-r)
3. y = a(x-p)³
Example
1. Sketch the graph y = (x-3)(x-1)(x+1)
Answer
X- intercepts
→ Make y = 0
(x-3)(x-1)(x+1) = 0
x = 3, 1, and -1
Y-intercepts
→ Make x = 0
y = (0-3)(0-1)(0+1)
y = 3
2. Write an equation for this graph.
Answer
X-intercepts are 2, -3, and -2.
Thus the equation is y = (x-2)(x+2)(x+3)
3. Write an equation of this graph.
X intercepts are three x=3
y = (x-3)(x-3)(x-3)
y = (x-3)³
In a nutshell
- Bold p,q,r are x-intercept and a is gradient.
- You can get x-intercept and y-intercept by putting y=0 and x=0 each.