# How do you find the important parts of the equation to graph the function # f(x) = x² - 2x -3#?

##### 1 Answer

The coordinates of the vertex are at

#### Explanation:

This problem nicely demonstrates the advantages of being able to view a quadratic function in STANDARD, VERTEX, and FACTORED form.

The function as given is in STANDARD form.

The **standard form** explicitly shows the **y-intercept** for the function.

If

The standard form also shows whether the parabola is downward-facing or upward-facing. If

Next, we can convert this function to its **vertex form** by completing the square. The advantage of the vertex form is that it explicitly shows you the **coordinates of the vertex**. If we have a parabola in vertex form

then the coordinates of the vertex will be at

For our function,

Finally we want to look at the function in **factored form** so that we can locate its **x-intercepts** if any exist. If a function is in factored form

and the x-intercepts will be at

The factored form for this function is

so the x-intercepts are at

We can put all of this information together to sketch the graph of our function.

graph{x^2-2x-3 [-5, 5, -5, 5]}