Question

Write a rule for the function in the form you would use to graph it

Answer 1

We are given the following function

`f(x)=-x^2+2x-2`

The standard form of a quadratic function is given by

`f(x)=ax^2+bx+c`

Comparing the given function with the standard form, we see that

a = -1

b = 2

c = -2

It is usually preferred to write the function in vertex form for graphing

The vertex form is given by

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

Where h is the vertex (maximum/minimum point of the graph) and is given by

`h=-(b)/(2a)=-(2)/(2(-1))=-(2)/(-2)=1`

Where k is given by

`\begin{gathered} k=f(h) \\ k=f(1) \\ k=-(1)^2+2(1)-2 \\ k=-1+2-2 \\ k=-1 \end{gathered}`

So, we have

a = -1

h= 1

k = -1

Therefore, the vertex form of the given function is

`\begin{gathered} f(x)=a(x-h)^2+k \\ f(x)=-(x-1)^2-1 \end{gathered}`