### 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 x

^{2}is positive, hence the graph is a U shape parabola with a minimum point.

__The minimum point of the graph__

By completing the square

$\begin{array}{l}f(x)={x}^{2}-x-12\\ f(x)={x}^{2}-x+{\left(\frac{1}{2}\right)}^{2}-{\left(\frac{1}{2}\right)}^{2}-12\\ f(x)={\left(x-\frac{1}{2}\right)}^{2}-\frac{1}{4}-12\\ f(x)={\left(x-\frac{1}{2}\right)}^{2}-12\frac{1}{4}\\ \\ \text{Minimumpoint=}(\frac{1}{2},-12\frac{1}{4})\end{array}$

For y-intercept, x = 0

$f(0)=(0{)}^{2}-(0)-12=-12$

For x-intercept, f(x) = 0

$\begin{array}{l}f(x)={x}^{2}-x-12\\ 0={x}^{2}-x-12\\ (x+5)(x-6)=0\\ x=-5\text{or}x=6\end{array}$

### Suggested Video

Graphs of Quadratic Function - khanacademyAlgebra - Quadratic Functions (Parabolas) - yaymath