Steps To Draw a Graph of Quadratic Equation

The example of problem:

1.  Draw a graph of quadratic equation  y= x²+2x-3

The steps to draw a graph are;

1.  Find the intersection point of y= x²+2x-3

2.  Remember there are two intersection points; on the x-axis and y-axis. To find the x-intercept set the equal to zero and solve 0=x²+2x-3

x²+2x-3=0

(x+3) (x-1)=0

x= -3  ,  x= 1

Since y=0 hence the intersection points (x.y) are (-3,0) and (1,0)

3.  To find the y-intercept set the x is zero and solve

y= x²+2x-3

y= (0)²+2(0)-3

y= -3

The intersection point is (0,-3)

4.  Then see the equation, is the graph upward or downward from α (constant) value. Positive it means upward and negative it means downward.

5.  Find the extreme point of the graph;

y= x²+2x-3

α=1 , b=2 , c= -3

x= -b/2α

x= -2/2(1) = -1

then find y-value, but find the determinant value first

D=b²-4αc

D=(2)²-4(1)(-3) = 16

y=D/4α

y=16/4(1)=4

Hence, the extreme point is (-1,4)

6. Sketch the curve throught all points that found. Don't forget that the graph is curve not a straight line, refer to the picture below;

created by Rina Fardiana