Apri’s 3rd posting - How to Graph Quadratic Function

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 = -⅕, 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!