Processing math: 100%
\

2.11 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)=x2x12

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)=x2x12f(x)=x2x+(12)2(12)212f(x)=(x12)21412f(x)=(x12)21214Minimum point = (12,1214)


For y-intercept, x = 0
f(0)=(0)2(0)12=12

For x-intercept, f(x) = 0
f(x)=x2x120=x2x12(x+5)(x6)=0x=5 or x=6



Suggested Video

Graphs of Quadratic Function - khanacademy

Algebra - Quadratic Functions (Parabolas) - yaymath

Leave a Comment