Question

What are the steps for plotting the graph of a function in standard form?

Answer 1

Let's suppose that we have the following function in standard form:

`f(x)=(x-1)^2-4`

We know that the general standard form of a function is:

`f(x)=a(x-h)^2+k`

then, in this case we have the following:

`\begin{gathered} a=1 \\ (h,k)=(1,-4) \end{gathered}`

Since the function is quadratic, the graph will be a parabola. The point (h,k) is where the vertex is located on the plane.

Then, we can find the roots of the function to see where the intersections with the x-axis are (if there are any):

`\begin{gathered} f(x)=(x-1)^2-4=0 \\ \Rightarrow(x-1)^2-4=0 \\ \Rightarrow x^2-2x+1-4=0 \\ \Rightarrow x^2-2x-3=0 \\ \Rightarrow(x+1)(x-3)=0 \\ \Rightarrow x_1=-1 \\ \text{and} \\ x_2=3 \end{gathered}`

we have that the parabola will cross the x axis when x=-1 and x=3, then, a sketch of the graph of f(x) would look like this: