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 x12 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 x12 0= x 2 x12 (x+5)(x6)=0 x=5 or x=6



Suggested Video

Graphs of Quadratic Function - khanacademy

Algebra - Quadratic Functions (Parabolas) - yaymath