There
are two kinds form of quadratic function;
-
y = ax2 + bx + c (it’s called “Common form”)
-
y = a(x – h)2 + k (it’s called “Vertex form”)
First, here
are the steps to graph the equation of y = ax2 + bx + c
1)
Check the value of a;
- If a > 0, then the graph will
be upward
-
If a < 0, then the graph will be downward
Another
thing that should we know:
- If |a| > 1 such as a = 2 or a
= -3, the graph will be “skinny”
-
If |a| < 1 such as a = ⅓ or a = -1/5, the graph will be “fat”
2)
Check the determinant (D = b2 – 4ac);
-
If D > 0, then the graph will intersect the x-axis in
two points (x1 , 0) and (x2 , 0)
-
If D = 0, then the graph will intersect the x-axis in one
point (x1 , 0)
-
If D < 0, then the graph will not intersect the
x-axis, and it’s called “definite positive”.
3)
Find the intersection point to the x-axis (hint: y = 0)
We can find x1 and x2
by using three methods that have been learned beforehand; factorization,
completing square, and ABC rules.
4)
Find the intersection point to the y-axis (hint: x = 0)
5)
Find the extreme point (-b/2a , -D/4a)
-
For the upward graph, it will have a minimum point (x = -b/2a as
the symmetry line,
and
y = -D/4a as
the minimum value)
-
For the downward graph, it will have a maximum point (x = -b/2a as the symmetry line,
and
y = -D/4a as the maximum value)
6)
Find some extra points for any x by substituting the x to
the equation y = ax2 + bx + c
7) Plot all points gained
to the Cartesian plane, and then connect all the points to be a curve. (hint:
make the curve as smooth as possible)
Second,
if you are given a quadratic equation of y = a(x – h)2 + k, it will
be easier to graph
1)
(h , k) is the vertex. (in Common form, it’s called
extreme value)
2)
Find some extra points for any x by substituting the x to
the equation y = a(x – h)2 + k
3) Plot all points gained
to the Cartesian plane, and then connect all the points to be a curve. (hint:
make the curve as smooth as possible)
Which
one is the easiest? It depends on which equation that you got! Happy Learning :)
