Vertex of the quadratic equation is the highest or the lowest point of the quadratic equation.
The given equation in the question is,
[tex]f(x) = x^2 - x +2[/tex]
Vertex of the quadratic equation is the highest or the lowest point of the quadratic equation.
To find the vertex of the equation we need to compare the given equation with the following equation.
[tex]f(x)=a(x-h)^2+k[/tex]
Here h and k are the vertex of the equation.
The given equation is,
[tex]f(x) = x^2 - x +2[/tex]
Rewrite the equation,
[tex]f(x) = x^2 - x +(\dfrac{1}2)^2} +2-(\dfrac{1}2)^2}[/tex]
[tex]f(x) = x^2 - x +\dfrac{1}{4} +2-\dfrac{1}4}[/tex]
[tex]f(x) =(x-\dfrac{1}{2} )(x-\dfrac{1}{2} )+2-\dfrac{1}{4}[/tex]
[tex]f(x) =(x-\dfrac{1}{2} )^2+\dfrac{7}{4}[/tex]
Thus the vertex of the quadratic equation is 1/2 and 7/4.
Learn more about the vertex of the quadratic equation here;
https://brainly.com/question/6356924
