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

User Natty
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that's the answers to these questions.
Marsha wants to determine the vertex of the quadratic function f(x) = x2 – x + 2. What-example-1
User Duc Vu Nguyen
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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).

User Shagymoe
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