Sketching the Graph of Quadratic Functions

Graphing Quadratic Function

If you are asked to sketch the graph of a quadratic function, you need to show
a. the shape of the graph
b. the maximum/minimum point of the graph
c. the x-intercept of the graph
d. the y-intercept of the graph


Example
Sketch the curve of the quadratic function f ( x ) = x 2 x 12

Answer:
The shape of the graph
Since the coefficient of x2 is positive, hence the graph is a U shape parabola with a minimum point.

The minimum point of the graph
By completing the square
f ( x ) = x 2 x 12 f ( x ) = x 2 x + ( 1 2 ) 2 ( 1 2 ) 2 12 f ( x ) = ( x 1 2 ) 2 1 4 12 f ( x ) = ( x 1 2 ) 2 12 1 4 Minimum point =  ( 1 2 , 12 1 4 )
For y-intercept, x = 0
f ( 0 ) = ( 0 ) 2 ( 0 ) 12 = 12
For x-intercept, f(x) = 0
f ( x ) = x 2 x 12 0 = x 2 x 12 ( x + 5 ) ( x 6 ) = 0 x = 5  or  x = 6



Suggested Video

Graphs of Quadratic Function - khanacademy

Algebra - Quadratic Functions (Parabolas) - yaymath

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