QUADRATIC GRAPH
CHANGE a, b, c · WATCH THE ROOTS
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The Parabola
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
-3
-2
-1
1
2
3
x
y
vertex
a
=
shape (narrow / wide)
b
=
left / right shift
c
=
up / down
1. Quadratic Formula
x = (−b ± √(b² − 4ac)) / 2a
roots:
2. Discriminant
D = b² − 4ac =
D > 0
2 real roots
D = 0
1 root (equal)
D < 0
no real roots
3. Remember
a > 0 → U shape (opens up)
Vertex: x = −b / 2a
MATRIC MATHS · QUADRATIC EQUATIONS · PUNJAB BOARDS
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