Respuesta :
Answer:
The vertex for each quadratic is [tex](x,y) = (1,1)[/tex]
Step-by-step explanation:
To determine the vertex for each quadratic,
The vertex of the [tex]x[/tex] coordinate can be determined using the formula,
[tex]x-vertex = \frac{-b}{2a}[/tex]
The standard form of the quadratic function is
[tex]f(x) = ax^{2} + bx + c[/tex]
Hence, for the given equation of the quadratic function,
[tex]f(x) = x^{2} -2x +2[/tex]
[tex]a = 1[/tex]
[tex]b = -2[/tex]
and [tex]c = 2[/tex]
Hence, [tex]x-vertex[/tex] becomes,
[tex]x-vertex = \frac{-b}{2a}[/tex]
[tex]x-vertex = \frac{--2}{2(1)}[/tex]
[tex]x-vertex = \frac{2}{2}[/tex]
∴[tex]x - vertex = 1[/tex]
This is the vertex for the [tex]x-coordinate[/tex]
To determine, the vertex for the [tex]y-coordinate[/tex]
We will put the value of the vertex of the [tex]x-coordinate[/tex] in the equation and write
[tex]y-vertex = x^{2} - 2x + 2[/tex]
Then,
[tex]y-vertex = (1)^{2} -2(1) + 2[/tex]
[tex]y-vertex = 1 - 2 +2\\y-vertex = 1[/tex]
This the vertex for the [tex]y-coordinate[/tex]
Hence, [tex](x,y) = (1,1)[/tex]
