Respuesta :
The function in vertex form is equivalent to [tex]\rm y = (x + 2/4)^2 + \frac{3}{4}[/tex].
What are quadratic equations?
A quadratic equation is an equation of degree 2 in other words.Quadratic equations have the form ax² + bx + c = 0 and are second-degree algebraic expressions.
The standard quadratic function with vertex (h, k) is ;
[tex]\rm y = a(x - h)^2 + k[/tex]
The general quadratic equation is found as;
[tex]\rm y = ax^2 + bx + c[/tex]
The value of h is given as;
[tex]\rm h = \frac{-b}{2a}[/tex]
For the given equation in the problem;
[tex]\rm y = x^2 + x + 1[/tex]
The value of the k is found by;
[tex]\rm y =( \frac{-1}{2}) ^2 - \frac{1}{2} + 1 \\\\ y= \frac{1}{4} - \frac{1}{2}+ 1 \\\\ y= \frac{1}{4}- \frac{2}{4}+ \frac{4}{4}\\\\ y= \frac{3}{4}[/tex]
So the vertex is at [tex]\frac{-2}{4}[/tex] and [tex]\frac{1}{4}[/tex] then the vertex form is:
[tex]y = (x +\frac{2}{4} )^2 + \frac{3}{4}[/tex]
Hence the functions in vertex form are equivalent [tex]\rm y = (x + 2/4)^2 + \frac{3}{4}[/tex].
To learn more about the quadratic functions refer to the link;
brainly.com/question/1214333
