Question

Marsha wants to determine the vertex of the quadratic function f(x) = x2 – x + 2. What is the function’s vertex?

Answer 1

that's the answers to these questions.

Answer 2

Answer: The required vertex of the given function is
`\left((1)/(2),(7)/(4)\right).`

Step-by-step explanation: Given that Marsha wants to determine the vertex of the following quadratic function :

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

We are to find the vertex of the function (i).

We know that

the form of a vertex function g(x) is as follows :

`g(x)=a(x-h)^2+k,` where (h, k) is the vertex.

From equation (i), we have

`f(x)\\\\=x^2-x+2\\\\=\left(x^2-2\imes x*(1)/(2)\right)+2\\\\\\=\left(x^2-2\imes x*(1)/(2)+\left((1)/(2)\right)^2\right)+2-\left((1)/(2)\right)^2\\\\\\=\left(x-(1)/(2)\right)^2+2-(1)/(4)\\\\\\=\left(x-(1)/(2)\right)^2+(8-1)/(4)\\\\\\=\left(x-(1)/(2)\right)^2+(7)/(4).`

Comparing the above with the vertex form of a function, we get

the vertex of the function f(x) is
`\left((1)/(2),(7)/(4)\right).`

Thus, the required vertex of the given function is
`\left((1)/(2),(7)/(4)\right).`