Dayah's Quadratic Function

 How to Draw a Graph of Quadratic Function

Written by:

Nurul Hidayah (2010110015)

     Quadratic Function is one of  topics in mathematics which students will be learned. The most basic quadratic is y = x². While the general form of a quadratic is “y = ax² + bx + c”.  Where a and b are called coefficient, x is a variable, and c is a constant. The students who understand this topic not only able to calculate this function but have to able to draw a graph of quadratic function. Actually, so many ways to draw it, but here I only give one way.

        I will give an example of the problem such as y = x² + 6x + 9. The steps to draw it as following below;

1.      Determine the vertex  (x,y).

Ø  Fisrt, we can find x using –b/2a. We know that a=1 and b=6. So, we can substitute 6 to b and 1 to a.

-b/2a = -6/2(1) = -3

            We get x is –3

Ø  Second, to find y, we can substitute -3 to y = x² + 6x + 9

y = (-3)² + 6(-3) + 9 = 0
We get y is 0
Hence, The vertex is (-3,0)

2.  We need additional points for our graph. Remember, three points will almost certainly not be enough points for graphing a quadratic. We should find many points.

x	y = x2 + 6x + 9
0	(0)2 + 6 (0) + 9 = 9
-1	(-1)2 + 6 (-1) + 9 = 4
-2	(-2)2 + 6 (-2) + 9 = 1
-4	(-4)2 + 6 (-4) + 9 = 1
-5	(-5)2 + 6 (-5) + 9 = 4
-6	(-6)2 + 6 (-6) + 9 = 9

3.  We have known the points we need to graph. So, we can plot all the points as following below.

4.   Now we can do our graph. Remember this is quadratic function, so do not connect the points with straight line segments. Draw a nicely smooth curving line passing neathly through the plotted points. Finally, we get the graph as following below.

It is easy, is not it? Let’s try it J