How to Sketch Parabolas
Mathematics In a Nutshell
Step
1. Find x intercept
2. Find y intercept
3. Find axis of symmetry
4. Find Vertex (x,y)
Example
y = x^2 - 2x - 8
Make form equation of y = (x- x1)(x - x2)
--> y = (x+2)(x-4)
1. Find x intercept
y= 0 , x=?
--> -2, 4
2. Find y intercept
x=0, y=?
--> 8
3. Find axis of symmetry
between x intercept
between -2 and 4
(-2) + 4 / 2
--> 1
4. Find vertex
x = 1 (axis of symmetry)
then, insert x = 1 in the this function of equation
y = (1+2)(1-4) = -9
Revision Question
1. y = (2-x)(x+1)
1. Find x intercept
Tip. think how to make x = 0, if y is equal to 0
0 = (2- x) (x + 1)
In this equation,
if x = 2
= (2 - 2) (2 + 1)
= 0 * 3
= 0
if x = -1
= (2 + 1)(-1 + 1)
= 3 * 0
= 0
--> -1, 2
2. Find y intercept
--> 2
3. Find axis of symmetry
--> 1/2
4, Find vertex
--> (1/2, 9/4)
2. y = (3 - x)^2
1. Find x intercept
insert y=0 in the equation
--> 3
2. Find y intercept
insert x=0 in the equation
--> 9
3. Find axis of symmetry
--> 3 (Because between 3 and 3 is 3)
4. Find vertex
Insert x = 3 and we can see this kinds of equations have result only y = 0
--> (3, 9)
3. y = -x(1 - x)
1. Find x intercept
--> 0, 1
2. Find y intercept
--> 0
3. Find axis of symmetry
--> 1/2
4. Find vertex
(1/2, 1/4)
