MBF3C
Date: _________________________
Graphing Quadratic Equations – The STEP Method
Consider the graph of the basic quadratic relation y = x 2
x
y = x2
-3
9
-2
4
-1
1
0
0
1
1
2
4
3
9
What is the
vertex?
Direction of
Opening?
(0, 0)
Up
What is the STEP Pattern?
(how do you move from point to
point, starting from the vertex?
it doesn’t matter if you go left or
right!)
Over 1
1 up
Over 1
3 up
Over 1
5 up
Over 1
1 x 2 = 2 up
Over 1
3 x 2 = 6 up
Over 1
5 x 2 = 10 up
Next consider the quadratic relation y = 2( x − 3)2 + 2
x
y = 2( x − 3)2 + 2
-1
34
0
20
1
10
2
4
3
2
4
4
5
10
What is the
vertex?
Direction of
Opening?
(3, 2)
UP
What is the STEP Pattern?
Adapted from OAME Support Resources for MBF3C – Quadratics I
MBF3C
Date: _________________________
How to Graph Using the Step Method
vertex
1. Identify and plot the __________________
(h, k)
pattern
2. Determine the step ___________________
(1a, 3a, 5a, 7a, etc.)
Plot
3. _____________
the step points ( over 1 up/down 1a,
over 1 up/down 3a,
over 1 up/down 5a)
axis of symmetry
4. Reflect each point across the ________________________________________
smooth
5. Draw a _________________
curve between points
EXAMPLE
1. Graph each quadratic relation without using a table of values.
Equation:
y = −3( x + 1)2 + 6
1
y = ( x − 3)2 − 2
2
What is the
vertex?
(-1, 6)
(3, -2)
Direction of
Opening?
DOWN
UP
What is the
Step Pattern?
1 x -3 = -3
3 x -3 = -9
5 x -3 =-15
1 x ½ = 0.5
3 x ½ = 1.5
5 x ½ = 2.5
Graph the
equation.
2. Complete the table
Equation
y = ( x − 2)2 + 1
Vertex
(2, 1)
Step Pattern
1, 3, 5
Direction of Opening
Up
y = −4( x + 4)2 + 64
(-4, 64)
-4, -12, -20
Down
y = – (x – 20)2 –10
(20, -10)
-1, -3, -5
Down
Adapted from OAME Support Resources for MBF3C – Quadratics I