# 2.5 Sketching the Graph of Quadratic Functions

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 $f\left(x\right)={x}^{2}-x-12$

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

For y-intercept, x = 0
$f\left(0\right)=\left(0{\right)}^{2}-\left(0\right)-12=-12$

For x-intercept, f(x) = 0